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In this paper we find the second generalized Hamming weight of someevaluation codes arising from a projective torus, and it allows to compute thesecond generalized Hamming weight of the codes parameterized by the edges ofany complete bipartite graph. Also, at the beginning, we obtain some resultsabout the generalized Hamming weights of some evaluation codes arising from acomplete intersection when the minimum distance is known and they arenon--degenerate codes. Finally we give an example where we use these results todetermine the complete weight hierarchy of some codes.

The second generalized Hamming weight of some evaluation codes arising from a projective torus