The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+324x^52+120x^53+208x^54+48x^55+265x^56+24x^57+32x^58+1x^72+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 0.726 seconds.