The concept of fluid antennas (FAs) has emerged as a promising solution to enhance the spectral efficiency of wireless networks, achieved by introducing additional degrees of freedom, including reconfigurability and flexibility. In this paper, we investigate the use of index-modulated (IM) transmissions within the framework of FA systems, where an FA position is activated during each transmission interval. This approach is motivated by the common characteristics exhibited by FAs and IM transmissions, which entails the use of a single radio-frequency chain. From this perspective, we derive a closed-form expression for the bit error rate of IM-FAs considering spatial correlation, and demonstrating superior performance compared to conventional IM systems. To enhance the performance of IM-FAs in correlated conditions, channel coding techniques are applied. We first analyze a set partition coding (SPC) scheme for IM-FAs to spatially separate the FA ports, and provide a tight performance bound over correlated channels. Furthermore, the spatial SPC scheme is extended to turbo-coded modulation where the performance is analyzed for low and high signal-to-noise ratios. Our results reveal that through the implementation of channel coding techniques designed for FAs and IM transmission, the performance of coded IM-FAs exhibits notable enhancements, particularly in high correlation scenarios.