Here is an approach that will get the results. It uses more of an iterative method.

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

my $seq = "AATGGTTTCTCCCATCTCTCCATCGGCATAAAAATACAGAATGATCTAA";

my @beg;
push @beg, $-[0] while $seq =~ /ATG/g;

my @end;
push @end, $+[0] while $seq =~ /T(?:AG|AA|GA)/g;

my @data;
for my $i (@beg) {
    for my $j (@end) {
        next if $j-$i < 6;    
        push @data, substr $seq, $i, $j-$i;
    }
}

print "$_\n" for @data;
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Output:

ATGGTTTCTCCCATCTCTCCATCGGCATAA
ATGGTTTCTCCCATCTCTCCATCGGCATAAAAATACAGAATGA
ATGGTTTCTCCCATCTCTCCATCGGCATAAAAATACAGAATGATCTAA
ATGATCTAA
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