That is very insecure. It's basically adding the same set of 13 numbers in a cycle to each 13th character of the plaintext. You can
eliminate the key from the cyphertext by calculating something along the lines of
$diff[$_] = $cyphertext[$_] - $cyphertext[$_+13] for 0..(@cyphertext
You then end up with this equivalence for all the chars in the plaintext, apart from the first and last 13:
$diff[$_] == $plaintext[$_] - $plaintext[$_+13];
From there it's fairly easy to deduce what @plaintext is, especially if a few chars of the plaintext are known or can be guessed.