Recently, fluid antenna (FA) systems integrated with reconfigurable intelligent surfaces (RIS) have attracted widespread attention as a highly promising technology for enhancing communication performance. Against this backdrop, to address the key limitations of existing FA index modulation, we propose a RIS enhanced code index modulation (CIM) scheme for grouped FA systems (GFA-RIS-CIM). Specifically, a joint space-code multi-dimensional index modulation scheme is proposed, which can achieve both superior bit error rate (BER) performance and higher data transmission rate compared to traditional FA one-dimensional index modulation schemes. We develop a grouped FA optimization strategy to mitigate the impact of spatial correlation on signal detection. We also propose a fast orthogonal code detection method for the proposed scheme to reduce complexity. We further theoretically analyze the overall system performance, including complexity and energy consumption. Finally, simulation results demonstrate that the GFA-RIS-CIM scheme outperforms existing one-dimensional and multi-dimensional index modulation schemes.