I believe you want: a) the match and also b) the position of the match? Modifying kschwab's regex..

#!/usr/bin/perl
use strict;
use warnings;

my $string = 'AAAA TTT GGGG CCCC AAAAAA CCCC ABAB CCC TTT TTTT GGGEGEE
+';

while ($string =~m/\b((\w)\2{2,6})\b/g)
{
    print "$-[1] $1 \n";   
}

__END__

#prints
0 AAAA  
5 TTT  
9 GGGG  
14 CCCC  
19 AAAAAA  
26 CCCC  
36 CCC  
40 TTT  
44 TTTT
[download]

Perlvar mentions @- and @+ although the explanation there is not completely clear.
In Perl 5.6.0 the "@-" and "@+" dynamic arrays were introduced that supply the indices of successful matches. @- is the beginning and @+ is the ending. $-[0] and $+[0] correspond to entire pattern, while $-[N] and $+[N] correspond to the $N ($1, $2, etc.) submatches.