Optical fiber communications require multiple-access schemes to access a shared channel among multiple users. The coherent ultrashort light pulse code-division multiple-access (CDMA) system is one such scheme, and it also offers asynchronous-access communication. This system usually employs 2-level, i.e., binary, m-sequences as signature codes because of their low correlation. If the number of active users is greater than the length of the m-sequence, i.e., code length, distinct m-sequences are used. However, the distinct 2-level m-sequences do not exhibit low correlation, resulting in performance degradation. We therefore propose a coherent ultrashort light pulse CDMA communication system with distinct 4-level, i.e., quaternary, m-sequences to improve system performance when the number of users is greater than the code length. We created the 4-level m-sequences from 2-level m-sequences, and assess the correlation of the 4-level m-sequences. We also theoretically derive the bit error rate (BER) of the proposed system taking into account multiple-access interference (MAI), beat noise, amplified spontaneous emission (ASE), shot noise, and thermal noise. The numerical results show that BER for distinct 4-level m-sequences is more than an order of magnitude smaller than that for distinct 2-level m-sequences. BER is limited by MAI and beat noise when the power of the received signal is high, otherwise BER is limited by ASE, shot noise, and thermal noise.