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The Space-Time Shift Keying (STSK) framework subsumes diverse Multiple-Input Multiple-Output (MIMO) schemes, offering a near-capacity performance at a reduced complexity. The STSK system's performance crucially depends on the dispersion matrix (DM) set used for encoding the transmitted symbols. We introduce a novel criterion, based on EXtrinsic Information Transfer (EXIT) chart analysis, for selecting capacity-approaching sets from candidate DMs, and a novel Genetic Algorithm (GA) for efficiently exploring the search space formed by the candidate DM sets. Our proposed GA allows obtaining DM sets that enhance the system's performance compared to a random selection, while simultaneously reducing the search algorithm's complexity.