Why not let Perl write the regex for you?

use Modern::Perl '2014';
use Algorithm::Permute;

my @elements = qw/ A C T G /;
my @permutations;
Algorithm::Permute::permute { push @permutations, ( join '(?:', @eleme
+nts ) . ')?)?)?'} @elements;
my $regex = join '|', @permutations;
$regex = qr/^(?:$regex)$/;

say "Testing";

for my $length ( 1 .. 4 ) {
    my $p =
      new Algorithm::Permute( [ qw/ A C T G A C T G A C T G A C T G X 
+/, ' ' ],
        $length );
    while ( my @res = $p->next ) {
        my $test = join( '', @res );
        print "$test\t";
        say $test=~ /$regex/ ? 'Accept' : 'Reject';
    }
}
[download]

Sample output:

Testing
A    Accept
C    Accept
T    Accept
G    Accept
(...)
X    Reject
     Reject
CA    Accept
AC    Accept
TC    Accept
CT    Accept
(...)
GA    Accept
AA    Reject
CC    Reject
(...)
AG    Accept
XC    Reject
CX    Reject
XT    Reject
(...)
CTGA    Accept
TCGA    Accept
TGCA    Accept
TGAC    Accept
CAGA    Reject
ACGA    Reject
(...)
[download]

The final regex for your pattern will then be /^$regex\s*,\s*$regex$/