  We introduce a simple, self-dual, rational, and $C_2$-cofinite vertex
operator algebra of CFT-type associated with a $\mathbb{Z}_k$-code for $k \ge
2$ based on the $\mathbb{Z}_k$-symmetry among the simple current modules for
the parafermion vertex operator algebra $K(\mathfrak{sl}_2,k)$. We show that it
is naturally realized as the commutant of a certain subalgebra in a lattice
vertex operator algebra. Furthermore, we construct all the irreducible modules
inside a module for the lattice vertex operator algebra.
