Could do something like this in python.

The below implementation:

• uses Hamming distance to rank order the changes in terms of distance.
• can weight transitions and transversions according to user input or will both be weighted as 1 if no weights are specified.
• will only include each pair of changes once, not twice.
• does not consider codons in the context of a nucleotide string, and as a result does not support deletion or insertion events, only substitutions
• returns a list of changes rank ordered by distance (smallest to largest differences).

    from itertools import combinations
    from collections import defaultdict

    # Step 1: Define codons and amino acids

    amino_acid_to_codons = { 'Ala': ['GCT', 'GCC', 'GCA', 'GCG'],
        'Arg': ['CGT', 'CGC', 'CGA', 'CGG', 'AGA', 'AGG'],
        'Asn': ['AAT', 'AAC'],
        'Asp': ['GAT', 'GAC'],
        'Cys': ['TGT', 'TGC'],
        'Gln': ['CAA', 'CAG'],
        'Glu': ['GAA', 'GAG'],
        'Gly': ['GGT', 'GGC', 'GGA', 'GGG'],
        'His': ['CAT', 'CAC'],
        'Ile': ['ATT', 'ATC', 'ATA'],
        'Leu': ['TTA', 'TTG', 'CTT', 'CTC', 'CTA', 'CTG'],
        'Lys': ['AAA', 'AAG'],
        'Met': ['ATG'],
        'Phe': ['TTT', 'TTC'],
        'Pro': ['CCT', 'CCC', 'CCA', 'CCG'],
        'Ser': ['TCT', 'TCC', 'TCA', 'TCG', 'AGT', 'AGC'],
        'Thr': ['ACT', 'ACC', 'ACA', 'ACG'],
        'Trp': ['TGG'],
        'Tyr': ['TAT', 'TAC'],
        'Val': ['GTT', 'GTC', 'GTA', 'GTG'],
        'Stop': ['TAA', 'TAG', 'TGA'] }

    def is_transition(nuc1, nuc2):
        transitions = {'A': 'G', 'G': 'A', 'C': 'T', 'T': 'C'}
        return transitions.get(nuc1) == nuc2

    def hamming_distance_weighted(codon1, codon2, transition_weight=1, transversion_weight=1):
        # Calculate the Hamming distance between two codons with optional weighting for transitions and transversions. 
        # codon1 (str): The first and second codons.
        # transition_weight (int): User-specified weight for transition changes.
        # transversion_weight (int): User-specified weight for transversion changes.
        # Returns: The weighted Hamming distance as an (int).
        distance = 0
        for c1, c2 in zip(codon1, codon2):
            if c1 != c2:
                if is_transition(c1, c2):
                    distance += transition_weight
                else:
                    distance += transversion_weight
        return distance

    def compute_and_rank_distances(transition_weight=1, transversion_weight=1):
        # Compute and rank the distances between all pairs of codons for all amino acids, using specified weights for 
        # transitions and transversions. Args:
        # transition_weight and transversion_weights (int): The weight for transitions and transversions (int).
        # Returns a list of tuples containing amino acid, codon1, amino acid, codon2, and distance, rank ordered by weight 
        # Hamming distance.
        distances = []
        processed_pairs = set() # Important: using a set prevents GAT -> GAC and GAC -> GAT from both appearing in the output.

        for aa1, codons1 in amino_acid_to_codons.items():
            for aa2, codons2 in amino_acid_to_codons.items():
                for codon1 in codons1:
                    for codon2 in codons2:
                        if codon1 != codon2 and (codon2, codon1) not in processed_pairs:
                            distance = hamming_distance_weighted(codon1, codon2, transition_weight, transversion_weight)
                            distances.append((aa1, codon1, aa2, codon2, distance))
                            processed_pairs.add((codon1, codon2))
        distances.sort(key=lambda x: x[4])     # Rank order the changes

        return distances

    # Example usage
    transition_weight = 1  # Set your desired weights here
    transversion_weight = 2 # If no weights are set, transitions and transversions will both be weighted as 1.

    ranked_distances = compute_and_rank_distances(transition_weight, transversion_weight)

    # Display the simplest changes
    numChangesToDisplay=50
    for aa1, codon1, aa2, codon2, distance in ranked_distances[:numChangesToDisplay]:
        print(f"{codon1} ({aa1}) -> {codon2} ({aa2}) with distance {distance}")