Multidimensional generalized quadrature index modulation scheme is proposed in this paper for conveying extra digital information with the aid of the space, radio frequency (RF) mirrors, and time indices. Explicitly, this proposed scheme cleverly combines another proposed time-indexed generalized quadrature spatial modulation (TI-GQSM) system with media-based modulation (MBM) transmission principle using RF mirrors, and it is referred to as TI-GQSM-MBM scheme. This scheme is attractive because of both the high data rate and the significant performance improvements that can be achieved. The system performance of the proposed schemes in terms of the bit error rate (BER) is evaluated and compared to the performance of the conventional schemes. Simulation results showed that a significant improvement is achieved by the TI-GQSM-MBM scheme as compared to that of TI-GQSM, time-indexed media-based modulation (TI-MBM) and the conventional generalized quadrature spatial modulation (GQSM) schemes for the same rate. It is also demonstrated that the proposed schemes are robust to channel estimation errors (CEEs) as compared to multidimensional generalized spatial modulation (GSM) schemes. Therefore, the proposed schemes can be effectively used as an alternative solution for various 5G and beyond wireless networks.