  We investigate the gauging of a $\mathbb{Z}_2$ symmetry in Narain conformal
field theories (CFTs) constructed from qudit stabilizer codes. Considering both
orbifold and fermionization, we establish a connection between $\mathbb{Z}_2$
gauging procedures and modifications of the momentum lattice by vectors
characterizing the $\mathbb{Z}_2$ symmetry. We also provide three-dimensional
interpretations of $\mathbb{Z}_2$ gaugings through abelian Chern-Simons
theories, which act as symmetry topological field theories.
