The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  1  1  1  1  2  1  1  1  1  1  4  1  2  4  8  1  4  4  1  2  1
 0 12  0  4  0  0  4 12  8 12  0 12  0 12  8 12  4  4  8  0  4  0  8  4  0 12 12  8  4  4 12 12  4  8  0  0  4  8  0
 0  0 12  4  0 12  4  8  4  4  0  0  0  4  4  8  4 12  4  0  4 12  4  8  4  0  8  0 12  0  0  8  4  0 12 12  8  4  8
 0  0  0  8  0  0  0  0  0  8  8  0  8  0  8  8  8  0  0  0  0  8  8  0  8  0  8  8  8  0  0  0  0  8  0  0  8  8  8
 0  0  0  0  8  0  0  8  8  8  8  0  0  8  8  8  0  0  8  8  8  8  0  0  8  0  0  8  0  0  0  0  8  0  0  8  0  0  0
 0  0  0  0  0  8  0  0  8  0  8  8  0  8  0  0  8  0  8  8  0  8  8  0  8  8  8  8  0  8  0  0  8  8  0  0  0  8  0
 0  0  0  0  0  0  8  0  0  0  8  0  8  8  8  8  0  8  8  8  0  0  8  8  8  8  8  0  8  0  8  0  8  0  8  0  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+33x^32+42x^33+128x^34+136x^35+291x^36+314x^37+830x^38+564x^39+851x^40+322x^41+286x^42+112x^43+81x^44+22x^45+29x^46+20x^47+23x^48+4x^49+5x^50+1x^54+1x^58

The gray image is a code over GF(2) with n=312, k=12 and d=128.
This code was found by Heurico 1.16 in 0.266 seconds.