  We construct fermionic conformal field theories (CFTs) whose spectra are
characterized by quantum stabilizer codes. We exploit our construction to
search for fermionic CFTs with supersymmetry by focusing on quantum stabilizer
codes of the Calderbank-Shor-Steane type, and derive simple criteria for the
theories to be supersymmetric. We provide several examples of fermionic CFTs
that meet the criteria, and find quantum codes that realize $\mathcal{N} =4$
supersymmetry. Our work constitutes a new application of quantum codes and
paves the way for the methodical search for supersymmetric CFTs.
