Automotive radar and communications are necessary components for future vehicles, allowing them to sense the environment and communicate with their surroundings. The joint design of both systems leads to potential gains in system size, power consumption, and spectrum efficiency. In this paper, we propose a dual function radar-communications system based on a multi-carrier frequency modulated continuous waveform MIMO radar. The proposed scheme transmits narrowband frequency modulated continuous waveform (FMCW) from a subset of transmit antennas in a randomized manner rather than utilizing all the elements simultaneously. The randomness is exploited to convey information in the form of index modulation by embedding the transmitted bits in the selection of carrier frequencies and antennas. The results show that the proposed radar scheme achieves a similar resolution performance compared with a wideband radar system operating with a large receive aperture. While for communications subsystem, the proposed scheme achieves better bit error rate performance than the system only exploiting phase modulation.