While I wouldn't recommend it, I didn't see the following approach:

my $string = 'AAATTTAGTTCTTAAGGCTGACATCGGTTTACGTCAGCGTTACCCCCCAAGTTATT
+GGGGACTTT';

my %max;
$string =~ s[(.)\1*][if ( length($&) > ($max{$1} // 0) ) {$max{$1} = l
+ength($&); }]eg;

for my $k (sort keys %max) {
    print"$max{$k} ", $k x $max{$k}, "\n";
}
[download]

output

3 AAA
6 CCCCCC
4 GGGG
3 TTT
[download]