Keeping your initial declaration of the hash, we can do:

my %CodonMap = ('GCA'=>'A', 'GCC'=>'A', 'GCG'=>'A', 'GCU'=>'A');
my @acodes = ();
for my $key (keys %CodonMap) {
    next unless $CodonMap{$key} eq 'A';
    push @acodes, $key;
}
print join ("\n", @acodes, '');
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There's probably a more efficient way, but at least you now have a working algorithm.