We construct a $(16, 3072, 3)$-code, a $(17,6144,3)$-code, an $(18,12288,3)$-code and a $(19,24576,3)$-code. Consequently, we get four new lower bounds: $A(16,3) \geq 3072$, $A(17,3) \geq 6144$, $A(18,3) \geq 12288$ and $A(19,3) \geq~24576$. Each of the codes consists of a union of cosets of a linear code. The constructions are the result of a computer search executing a tabu search algorithm.

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