The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+45x^32+56x^33+159x^34+274x^35+570x^36+980x^37+1286x^38+1522x^39+1286x^40+948x^41+547x^42+230x^43+134x^44+60x^45+48x^46+22x^47+12x^48+4x^49+5x^50+2x^54+1x^58

The gray image is a code over GF(2) with n=312, k=13 and d=128.
This code was found by Heurico 1.16 in 0.727 seconds.