A few more examples would be good, but this produces the desired output for the two you given:

C:\test>876075
AGRTGAXWXX : [ AGRTGA ]
ACRMGAHKMAHGTXX : [ GAHKMAHGT, ACRMGAHKMA ]
[download]

#! perl -slw
use strict;
use Data::Dump qw[ pp ];

sub maxMatches {
    my $s = shift;
    my %uniq;

    LOOP: for my $o ( 0 .. length( $s ) - 10 ) {
        my( $match ) =  $s =~ m[.{$o}([ACGT].{0,8}[ACGT])];
        m[$match] and next LOOP for keys %uniq;
        $uniq{ $match }++;
    }
    return keys %uniq;
}

while( <DATA> ) {
    chomp;
    printf "$_ : [ %s ]\n", join ', ', maxMatches( $_ );
}

__DATA__
AGRTGAXWXX
ACRMGAHKMAHGTXX
[download]