The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  1  1  1  4  1  1  2  0  1  1  1  2  4  1  2  2
 0 12  0 12  0 12  0 12  8  4  0 12  0 12  8  4  0  0  0  8  0 12 12 12  4 12 12  4  8 12  4 12  4  4 12 12 12 12  0
 0  0  8  0  0  0  0  0  8  0  0  0  8  8  8  8  0  0  8  8  8  0  8  0  0  0  8  0  0  0  0  8  0  8  8  8  8  0  0
 0  0  0  8  0  0  0  0  0  8  0  8  8  8  8  0  0  8  8  8  0  0  0  0  8  8  0  8  8  8  0  0  8  8  0  8  8  0  0
 0  0  0  0  8  0  0  0  0  0  8  0  8  0  8  0  0  8  8  0  0  0  8  8  8  8  8  8  0  0  0  8  8  8  8  0  8  0  8
 0  0  0  0  0  8  0  0  0  0  0  8  0  8  0  8  8  8  8  8  8  0  8  8  0  8  0  0  8  8  8  8  0  8  0  8  8  0  8
 0  0  0  0  0  0  8  0  8  0  8  8  8  0  0  8  8  8  8  0  8  8  0  0  8  8  0  8  8  0  0  8  0  0  8  0  8  8  8
 0  0  0  0  0  0  0  8  0  8  8  8  0  0  8  8  0  0  8  8  8  8  8  0  8  8  8  0  8  8  8  0  0  8  8  0  0  0  8

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

Homogenous weight enumerator: w(x)=1x^0+81x^32+120x^34+352x^36+256x^37+976x^38+512x^39+1040x^40+256x^41+280x^42+157x^44+32x^46+22x^48+10x^52+1x^60

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 0.283 seconds.