Given K users simultaneously active, an Optical CDMA (OCDMA) receiver needs to discriminate among K codes. Since the number of available codes C is always C≫K at any given time for an asynchronous OCDMA system employing quasi-orthogonal codes, there is always a set of unused codes and these codes can be exploited to increase the spectral efficiency of the system. This can be accomplished by exclusively assigning to each user a set of M codes which represent a log2(M)-tuple of bits so that each user effectively uses a multidimensional modulation (multiple information bits per code are conveyed). In this paper, we analyze the performance of such a system, and find that an upper bound on the probability of error can be expressed in terms of the performances of the conventional case where one code only per user is employed. Moreover, we also find that, under certain conditions, the multidimensional modulation here proposed allows us to obtain higher spectral efficiency, higher power efficiency, and lower bit-error rate (BER) than conventional OCDMA, which employs one code per user.