  The design of binary error-correcting codes is a challenging optimization
problem with several applications in telecommunications and storage, which has
also been addressed with metaheuristic techniques and evolutionary algorithms.
Still, all these efforts focused on optimizing the minimum distance of
unrestricted binary codes, i.e., with no constraints on their linearity, which
is a desirable property for efficient implementations. In this paper, we
present an Evolutionary Strategy (ES) algorithm that explores only the subset
of linear codes of a fixed length and dimension. To that end, we represent the
candidate solutions as binary matrices and devise variation operators that
preserve their ranks. Our experiments show that up to length $n=14$, our ES
always converges to an optimal solution with a full success rate, and the
evolved codes are all inequivalent to the Best-Known Linear Code (BKLC) given
by MAGMA. On the other hand, for larger lengths, both the success rate of the
ES as well as the diversity of the evolved codes start to drop, with the
extreme case of $(16,8,5)$ codes which all turn out to be equivalent to MAGMA's
BKLC.
