  We study a new class of codes over Z_2 x Z_2 which we call L-codes. They
arise as a natural fifth step in a series of analogies between Kleinian codes,
binary codes, lattices and vertex operator algebras. This analogy will be
explained in detail. We classify self-dual L-codes up to length 10 and provide
tables for these codes and their weight enumerators up to length 4. We also
discuss extremal codes for which a nearly complete classification is obtained.
