In this paper, we proposed a novel system called the Joint Carrier-Time-Code-Sort Index Modulation Differential Chaos Shift Keying (JCTCSIM-DCSK) system, designed to achieve ultra-high data rate transmission. This system incorporates four distinct forms of index modulation: carrier, time slot, Walsh code, and sort. Particularly noteworthy is the introduction of the sort index, a unique feature within DCSK-related systems. The sort index is applied by arranging the selected indices from the code index in sequential order and placing them within the unselected time slots of inactive subcarriers. Furthermore, we present a joint demodulation algorithm at the receiver capable of simultaneously recovering time slot, Walsh code, and sort indices after carrier recovery. Furthermore, we have implemented noise reduction techniques at the receiver to improve the bit error rate (BER) performance. Our analysis covers the system’s data rate, spectral efficiency, and complexity, comparing these factors against those of similar systems. Additionally, we formulate theoretical BER equations for the JCTCS-IM-DCSK system in the presence of additive white Gaussian noise (AWGN) and multipath Rayleigh fading channels. The simulation results not only confirm the precision of the theoretical BER expressions but also showcase our system’s superior BER performance when compared with similar systems under equivalent conditions.