The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  2  1  2  8  1  1 12  1  1  1  8  1  2  1  1  4  2  4  2  1  0  1  4
 0  2  0  6  4  6 12  2  6 14  8 12  0  2  4  2  6 10 14  2  4 10  2  6  6  0  2  2  2  8 12  2  4  4  6 10  0  2  2
 0  0 12  0  4  0  0  8  4 12  0  4  4 12  8  8  0 12  4 12  0  0  8  4  8 12  8  0  4 12  0  0  0 12  8  4  8 12 12
 0  0  0 12  0  0  0 12  4  8 12 12  4  8 12  8  0 12  8  8  4  8  0  0  4  4 12  0  0  8  0  4 12  0  8 12  4  8  8
 0  0  0  0  8  0  0  0  0  0  0  0  8  8  0  0  8  0  8  0  8  8  0  0  0  8  8  8  0  8  8  0  8  8  8  0  0  8  0
 0  0  0  0  0  8  0  8  0  8  8  8  8  8  8  8  8  8  0  0  8  0  0  8  8  0  0  0  8  8  0  8  0  8  8  0  0  0  8
 0  0  0  0  0  0  8  0  0  0  0  8  8  8  8  0  0  8  8  0  8  0  8  8  8  8  0  8  8  0  8  8  0  8  0  8  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+159x^32+152x^33+438x^34+604x^35+1243x^36+1872x^37+2278x^38+2900x^39+2310x^40+1944x^41+1198x^42+580x^43+372x^44+128x^45+106x^46+12x^47+66x^48+12x^50+9x^52

The gray image is a code over GF(2) with n=312, k=14 and d=128.
This code was found by Heurico 1.16 in 3.22 seconds.