The differential chaos shift keying with code index modulation (CIM-DCSK) using Walsh codes can increase the data rate, but error rate performance degrades over practical multipath channel with high delay spread. To tackle this drawback, this paper proposes a parallel CIM-DCSK (PT-CIM-DCSK), where the first time slot is used to transmit the chaotic reference sequence, and the second slot is used to transmit the multiple sequences carrying data bits. In particular, multiple $q$ chaotic sequences are added for data transmission in parallel, and each sequence is modulated by CIM-DCSK with $m_{c}$ bits. By exploiting the quasi-orthogonal characteristics of permuted chaotic signals, the interference between $q$ sequences can be remarkably suppressed. In this way, given the data rate, PT-CIM-DCSK can achieve a larger length of Walsh segment than the CIM-DCSK, since its parallel transmission compensates the rate. In addition, the error performance of the proposed scheme over the multipath Rayleigh fading channel is theoretically analyzed. The theoretical and consistent simulation results demonstrate that the PT-CIM-DCSK can obtain significant performance gains over the conventional CIM-DCSK, and the gain can be up to 5 dB in multipath fading channel with high delay. This is because the larger Walsh segment of PT-CIM-DCSK provides the enhanced robustness against multipath effect. The performance superiority of the proposed scheme is further verified in practical ultra-wideband (UWB) wireless industrial scenarios, which suggests promising for low-cost and low-complexity wireless communication applications.