In this paper, a new high-data rated and energy-efficient hexagonal quadrature amplitude modulation aided media-based modulation scheme, called HQAM-MBM, is proposed for the next-generation communication systems. In MBM, mirror activation patterns (MAPs) of a reconfigurable antenna have been used to convey extra information in addition to conventional modulated symbols. Therefore, the MBM is seen as a promising index modulation (IM) scheme for the next generation of high-data rated communication systems. On the other hand, the HQAM constellation scheme is more energy-efficient than traditional QAM but also has a similar performance at high signal-to-noise ratio (SNR) values. Hence, the HQAM technique can appear as a promising energy-efficient scheme for 5G and beyond networking systems. From this point forth, it has been found appropriate to propose the rational HQAM-MBM technique, which uses an energy-efficient HQAM constellation instead of a traditional QAM constellation, and also carries additional information with the indices of the MAPs of a reconfigurable antenna. Besides, it has been shown via computer simulations that the HQAM-MBM system has lower transmission energy than QAM-MBM systems. Performance analysis of the HQAM-MBM scheme is evaluated on Rayleigh fading channels.