This paper proposes a high-throughput short reference differential chaos shift keying cooperative communication system with the aid of code index modulation, referred to as CIM-SR-DCSK-CC system. In the proposed CIM-SR-DCSK-CC system, the source transmits information bits to both the relay and destination in the first time slot, while the relay not only forwards the source information bits but also sends new information bits to the destination in the second time slot. To be specific, the relay employs an $N$-order Walsh code to carry additional ${{\log }_{2}}N$ information bits, which are superimposed onto the SR-DCSK signal carrying the decoded source information bits. Subsequently, the superimposed signal carrying both the source and relay information bits is transmitted to the destination. Moreover, the theoretical bit error rate (BER) expressions of the proposed CIM-SR-DCSK-CC system are derived over additive white Gaussian noise (AWGN) and multipath Rayleigh fading channels. Compared with the conventional DCSK-CC system and SR-DCSK-CC system, the proposed CIM-SR-DCSK-CC system can significantly improve the throughput without deteriorating any BER performance. As a consequence, the proposed system is very promising for the applications of the 6G-enabled low-power and high-rate communication.