  A Butson-Hadamard matrix H is a square matrix of dimension n whose entries
are complex roots of unity such that HH*= nI. In the first part of this work,
some new results on generalized Gray map are studied. In the second part, codes
obtained from Butson-Hadamard matrices and some bounds on the minimum distance
of these codes are proved. In particular, we show that the code obtained from a
Butson-Hadamard matrix meets the Plotkin bound under a non-homogeneous weight.
We also give the parameters of some code families which are obtained from
modified Butson-Hadamard matrices under a (non)homogeneous Gray map.
