  We construct a map between a class of codes over $F_4$ and a family of
non-rational Narain CFTs. This construction is complementary to a recently
introduced relation between quantum stabilizer codes and a class of rational
Narain theories. From the modular bootstrap point of view we formulate a
polynomial ansatz for the partition function which reduces modular invariance
to a handful of algebraic easy-to-solve constraints. For certain small values
of central charge our construction yields optimal theories, i.e. those with the
largest value of the spectral gap.
