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An increasing number of hybrid mobile systems comprising a satellite and a terrestrial component are becoming standardized and realized. The next generation of these systems will employ higher dimensions adopting multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) techniques. In this work, we build upon recent studies of dual polarization MIMO for each component and propose the use of full-rate full-diversity (FRFD) codes adopting a space-frequency paradigm. We also propose a scheme taking advantage of the separation between the subcarriers to enhance the coding gain. By critically assessing the different options for the 4 transmit, 2 receive hybrid scenario taking into account system and channel particularities, we demonstrate that the proposed scheme is a solution for enhancing the performance of next generation hybrid mobile satellite systems.