We study the problem of finding shortest self-orthogonal embeddings of a given code which have the largest possible minimum distance by employing a constraint-preserving genetic algorithm. We show that the orthogonal group is generated by transvections corresponding to weight-four vectors. Using this result together with the fact that all shortest self-orthogonal embeddings can be obtained through the action of the orthogonal group, we construct a genetic algorithm in which each chromosome is represented by a sequence of weight-four vectors. Applying our algorithm to codes with dimensions $9\le k\le 15$ and lengths $22\le n\le 256$, we obtain 280 inequivalent optimal self-orthogonal codes. In particular, we obtain 34 codes with new parameters and 100 codes which are inequivalent to previously known codes with the same parameters.

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