$_ = 'acgnt' x 4;
push @strings, "$1$2"     while /.*(.).*(.)(?(?{$_{"$1$2"}++})^)/;
push @strings, "$1$2$3"   while /.*(.).*(.).*(.)(?(?{$_{"$1$2$3"}++})^)/;
push @strings, "$1$2$3$4" while /.*(.).*(.).*(.).*(.)(?(?{$_{"$1$2$3$4"}++})^)/;

print join $/, @strings;