The original DQRUMA/MC-CDMA protocol may suffer severe code collisions due to a limited number of request codes. An enhanced DQRUMA/MC-CDMA protocol using minislots for request accesses is proposed to reduce request collisions. In the proposed protocol, request attempts are transmitted concurrently with data packets of other calls. A random scheme (Scheme I) and a designated scheme (Scheme II) are distinguished depending on the methods which select a request code and a request minislot based on a lattice pool for request accesses (LPRA). Both schemes yield low request access delays due to few or no collisions during request accesses. In Scheme I one of request minislots is selected with a randomly chosen code, while in Scheme II the minislot and the code uniquely used in request attempts can resolve a code collision problem during request accesses. The performance of the proposed protocol is evaluated by simulation and the result shows that the proposed protocol outperforms the original DQRUMA/MC-CDMA protocol in terms of average total delay.