Just in case you need offsets as well, here's a solution for that.

use strict;
use warnings;

use feature qw{ say };

my $string
   = q{AAATTTAGTTCTTAAGGCTGACATCGGTTTACGTCAGCGTTACCCCCCAAGTTATTGGGGACT
+TT};
my @matches;
push @matches, [ length $1, $1, $-[ 0 ] ]
   while $string =~ m{(([ACGT])\2+)}g;

say qq{Found $_->[ 1 ], length $_->[ 0 ] at offset $_->[ 2 ]} for
   sort { $b->[ 0 ] <=> $a->[ 0 ]
          ||
          $a->[ 1 ] cmp $b->[ 1 ]
          ||
          $a->[ 2 ] <=> $b->[ 2 ]
        } @matches;
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The output, sorted ascending offset within ascending letter within descending length.

Found CCCCCC, length 6 at offset 42
Found GGGG, length 4 at offset 56
Found AAA, length 3 at offset 0
Found TTT, length 3 at offset 3
Found TTT, length 3 at offset 27
Found TTT, length 3 at offset 62
Found AA, length 2 at offset 13
Found AA, length 2 at offset 48
Found GG, length 2 at offset 15
Found GG, length 2 at offset 25
Found TT, length 2 at offset 8
Found TT, length 2 at offset 11
Found TT, length 2 at offset 39
Found TT, length 2 at offset 51
Found TT, length 2 at offset 54
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I hope this is helpful.