This script works:

#!/usr/bin/perl
use strict;
use warnings;
use Bio::EnsEMBL::Registry;

my $registry = "Bio::EnsEMBL::Registry";

$registry->load_registry_from_db(
   -host => 'ensembldb.ensembl.org',
   -user => 'anonymous'
);

my $gene_adaptor = $registry -> get_adaptor('Mouse', 'Core', 'Gene');

my $gene_name = "Optn";

my @genes = @{ $gene_adaptor->fetch_all_by_external_name($gene_name) };

while (my $gene = shift @genes){

    print $gene->external_name, ", ", $gene->stable_id, "\n";

    my @transcripts = @{ $gene->get_all_Transcripts };

    while (my $transcript = shift @transcripts) {

        if ($transcript->biotype eq "processed_pseudogene"
        or $transcript->biotype eq "IG_C_pseudogene"
        or $transcript->biotype eq "IG_J_pseudogene"
        or $transcript->biotype eq "IG_V_pseudogene"
        or $transcript->biotype eq "polymorphic_pseudogene"
        or $transcript->biotype eq "pseudogene"
        or $transcript->biotype eq "unprocessed_pseudogene"
        or $transcript->biotype eq "TR_J_pseudogene"
        or $transcript->biotype eq "TR_V_pseudogene"
        ) {
        print $transcript->stable_id, "\n";
        }
    }
}

Edit to put in different genes, change what you print out etc. Also, check the possible biotypes (which, as Khader says, you can find in BioMart) and add any more that you think are relevant to your search.

While some pseudogenes are transcribed, most are not. I'm not sure where that leaves the Ensembl transcripts. HGNC curate some psuedogenes but not many. You can cluster hypothetical ORFs but as most should have frameshifts, stops or other transcription/translation breakers that wont be easy

pseudogene.org has outdated annotations - corresponding to the May 2004. genome built (unless I couldn't find the recent ones, which is highly plausible), and it requires 2 liftovers to get the coordinates to mm9 - mm10

Dear Khader, thank you so much for your answer, but I am already aware that I can find a list of all of the pseudogenes in a certain genome.

Let me rephrase my question: given a gene (say Optn), is there an easy way to find its related pseudogenes?