Families of codes, such as group codes, constacyclic, and skew cyclic codes, which were independently suggested, turn out to be special instances of the general family of crossed product codes. Under this framework, the ambient code spaces are classified here with respect to Hamming-isometry in cohomological terms. This classification is demonstrated by two families of examples. We also determine when crossed products belonging to these families are semisimple and, in particular, when they admit only trivial codes.