The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  1  0  1  1 12  1  6  1  1  1 10  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  8  6 14 12  4
 0  1  3  6  5  1 12 15  1 10  9  1  0  3  1  6 15  1  5  1 12 10  9  1  0  6 12  3  5 15  9 14 10  8  4  2 11 13  7  1  0  8  3 14 11 13  6  5  1  1  1  1  1  1
 0  0  8  0  8  0  8  0  8  8  0  8  0  0  0  8  8  8  0  0  8  0  8  8  8  0  0  0  0  8  8  8  0  8  0  8  8  8  0  0  8  8  8  0  8  0  8  8  8  8  8  8  0  0
 0  0  0  8  8  8  8  0  0  0  8  8  8  8  8  8  8  8  0  0  0  0  0  0  8  0  8  0  8  0  8  0  8  0  0  8  8  0  8  0  0  8  8  8  0  8  0  0  0  8  0  8  8  8

generates a code of length 54 over Z16 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+360x^52+304x^54+354x^56+2x^60+2x^68+1x^80

The gray image is a code over GF(2) with n=432, k=10 and d=208.
This code was found by Heurico 1.16 in 1.8 seconds.