Multicarrier CDMA (MC-CDMA) has become a promising candidate for future wireless multimedia communications for its robustness to frequency-selective fading and its flexibility in handling multiple data rates. Among different multirate access schemes, multicode MC-CDMA is attractive for its high performance, good flexibility in rate matching, and low complexity. However, its performance is limited by self-interference (SI) and multiuser interference (MUI). In this paper, a zero-forcing successive interference cancellation (ZF-SIC) receiver is used to mitigate this problem for multicode MC-CDMA. Furthermore, optimal power distribution control (PDC), which minimizes each user's bit error rate (BER), is considered. Our results show that, in correlated Rayleigh fading channels, the ZF-SIC receiver integrated with the optimal PDC dramatically improves the performance of the multicode MC-CDMA system in comparison with other receivers proposed in the literature. Moreover, the optimal PDC significantly outperforms the PDC based on equal BER criterion, particularly under a short-term transmit power constraint.