Maybe this will help get you started.

Here's a script to simulate input:

#!/usr/bin/env python

import sys
from random import randint

chrs = ['chr1',
        'chr2',
        'chr3',
        'chr4',
        'chr5',
        'chr6',
        'chr7',
        'chr8',
        'chr9',
        'chr10',
        'chr11',
        'chr12',
        'chr13',
        'chr14',
        'chr15',
        'chr16',
        'chr17',
        'chr18',
        'chr19',
        'chr20',
        'chr21',
        'chr22',
        'chrX',
        'chrY']

bounds = [248956422,
          242193529,
          198295559,
          190214555,
          181538259,
          170805979,
          159345973,
          145138636,
          138394717,
          133797422,
          135086622,
          133275309,
          114364328,
          107043718,
          101991189,
          90338345,
          83257441,
          80373285,
          58617616,
          64444167,
          46709983,
          50818468,
          156040895,
          57227415]

binsize = 1000000
maxmutations = 100

for chri,chrv in enumerate(chrs):
    bound = bounds[chri]
    chr = chrv
    for start in range(0, bound, binsize):
        mutations = randint(0, maxmutations)
        sys.stdout.write('%s\t%d\t%d\t.\t%d\n' % (chr, start, start + binsize, mutations))

You might run it like so, to get some test input:

$ ./simulateMutations.py | sort-bed - > mutations.bed

Then you could plot it with something like the following:

#!/usr/bin/env Rscript

suppressPackageStartupMessages(require(optparse))

option_list = list(
  make_option(c("-i", "--input"), action="store", default=NA, type='character', help="input filename"),
  make_option(c("-o", "--output"), action="store", default=NA, type='character', help="output filename")
)
opt = parse_args(OptionParser(option_list=option_list))

d <- read.table(opt$input, header=F, stringsAsFactor=T, col.names=c("chr", "start", "stop", "id", "mutations"))
d$chr <- factor(d$chr, levels = c('chr1', 'chr2', 'chr3', 'chr4', 'chr5', 'chr6', 'chr7', 'chr8', 'chr9', 'chr10', 'chr11', 'chr12', 'chr13', 'chr14', 'chr15', 'chr16', 'chr17', 'chr18', 'chr19', 'chr20', 'chr21', 'chr22', 'chrX', 'chrY'))
d <- with(d, d[order(chr),])

library(ggplot2)
pdf(opt$output)

p <- ggplot(data=d, aes(x=start, y=1)) +
  facet_grid(chr ~ ., switch='y') +
  geom_tile(aes(fill=mutations)) +
  theme(axis.title.y=element_blank(),
        axis.text.y=element_blank(),
        axis.ticks.y=element_blank(),
        strip.text.y = element_text(angle = 180)) +
  scale_fill_gradientn(colours = rainbow(5), breaks=seq(min(d$mutations),max(d$mutations),(max(d$mutations)-min(d$mutations))/4))

print(p)
dev.off()

You might run it like so:

$ ./plotMutations.Rscript -i mutations.bed -o mutations.pdf

This will make a figure that looks like this:

Pretty close to what you want, but not exact. You could use Stack Overflow and other resources to tweak the ggplot2 code to do what you need for your particular dataset: change axis and panel labels, sort order, color gradient, breaks, etc.