In this paper, we derive the distribution of Multiple Access Interference (MAI) power for wireless Code Division Multiple Access (CDMA) ad hoc networks operating in a general Nakagami-m fading channel model. Furthermore, we propose a Multi-Code Multi-Packet Transmission (MCMPT) scheme for it to increase the performance, in terms of the expected forward progress. Based on the instantaneous good channel conditions in a Nakagami-m fading channel, a node can initiate flexible number of parallel transmission of multiple packets on multiple codes. Numerical results show that adaptive MCMPT considering varying channel conditions not only outperforms the nonadaptive Conventional Packet Transmission (CPT), but also achieves better progress improvement with the increasing values of parametermin a slowly-varying Nakagami-m fading channel.