In this paper, we propose a faster-than-Nyquist (FTN) signaling-aided space-time multi-mode index modulation (IM) scheme with a low-complexity Gaussian message passing (GMP) based receiver. The advantages of spatial domain IM, time-domain IM relying on multiple modes and FTN signaling are explored. Specifically, multi-mode IM is employed in time domain by activating all time slots, hence the spectral efficiency is improved substantially compared to its single-mode counterpart. Meanwhile, the transmission rate is further increased by utilizing FTN signaling. At the receiver, based on the state-space model of IM symbols, a two-layer Forney style factor graph (FG) representation for the system is constructed to exploit the truncated inter-symbol interference structure imposed by FTN. Belief propagation is invoked to update the messages over the FG. The discrete messages from the channel decoder are properly approximated to be Gaussian for reducing the complexity of joint detection of multidimensional index modulated symbols. Moreover, the extrinsic information from the equalizer is derived with a concise representation. A low-complexity log-likelihood ratio calculation method is further proposed, where the search space is significantly reduced using a Gaussian mixture model. Simulation results demonstrate that the proposed scheme outperforms the existing schemes in terms of bit error rate given the same spectral efficiency. The outstanding performance and low complexity of the proposed GMP-based receiver are also verified by comparisons with existing methods.