On the basis that you're more interested in getting the results rather than doing it yourself you may want to use the String::Combination module on CPAN which does what you need.

The following code seems to do the job..

#!/usr/bin/perl
use strict;
use warnings;
use String::Combination;

# Get all the combinations of bases which have a prescribed length.
my $length=2;
my @combinations=String::Combination::combination('atcg',$length);

# Output the results.
print "$_\n" for @combinations;
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