  Twisted permutation codes, introduced recently by the second and third
authors, are frequency permutation arrays. They are similar to repetition
permutation codes, in that they are obtained by a repetition construction
applied to a smaller code. It was previously shown that the minimum distance of
a twisted permutation code is at least the minimum distance of a corresponding
repetition permutation code, but in some instances can be larger. We construct
two new infinite families of twisted permutation codes with minimum distances
strictly greater than those for the corresponding repetition permutation codes.
