The generator matrix

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

generates a code of length 39 over Z16 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+151x^32+104x^33+656x^34+1092x^35+2099x^36+4232x^37+4846x^38+6492x^39+4730x^40+4344x^41+2110x^42+1052x^43+556x^44+88x^45+122x^46+4x^47+78x^48+10x^50+1x^52

The gray image is a code over GF(2) with n=312, k=15 and d=128.
This code was found by Heurico 1.16 in 7.26 seconds.