Update: The post above, in its entirety, originally read:

Your addition of unrequested functionality is what prompted my question. There was no unstated rule.

And was silently modified after the fact, without notification, in typically unhanded, duplicitous, and utterly dishonourable fashion. Presumably an attempt to try and save face.

Sorry, but the OPs own code would remove all duplicates sequences found, regardless of where they were found.

my %uniq=();
my $string = 'ACRMGAHKMAHGTXX';

      substr($string, $_, 10 ) =~ m[([AGTC].{0,8}[AGTC])]
      and ++$uniq{ $1 }
      for 0 .. length( $string )-1;

for my $key (keys %uniq){
    print $key, "\n";
}
[download]

In the absence of any specific discussion, the OPs code is the spec. You opened that discussion, and I up-voted you for doing so, but there is no mention of that requirement in the OPs post. Neither in the stated "conditions", nor the worked examples.

A requirement, not discussed is "unstated".