The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1  1  1  1  1  2  1  1  1  4  1  2  1  1  1  1  1  1  2  1  1
 0 12  0 12  0 12  0  4  8 12  0 12  0 12  4 12  8 12  4  0  8  0  8 12  0  8 12 12  4 12  0  0  8 12  8  8 12  0  0
 0  0  8  0  0  0  0  0  8  0  0  0  8  8  0  0  8  8  8  0  8  8  0  0  0  0  8  8  8  8  0  8  0  0  8  0  8  0  0
 0  0  0  8  0  0  0  8  0  0  0  8  0  8  8  0  0  8  8  8  8  8  8  0  8  8  8  8  8  8  8  8  8  8  8  8  8  8  0
 0  0  0  0  8  0  0  0  0  8  8  8  0  8  0  8  8  0  8  8  8  0  8  0  8  0  0  8  8  0  8  8  0  0  0  0  0  0  0
 0  0  0  0  0  8  0  8  0  8  8  0  8  8  0  0  0  8  0  0  8  0  8  0  8  8  0  8  0  8  0  0  0  8  8  0  8  0  0
 0  0  0  0  0  0  8  0  8  0  8  8  0  0  8  0  8  8  8  0  8  8  0  0  8  8  0  0  0  0  8  8  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+25x^32+62x^34+32x^35+98x^36+64x^37+464x^38+576x^39+459x^40+64x^41+92x^42+32x^43+48x^44+16x^46+2x^48+6x^50+5x^52+1x^56+1x^68

The gray image is a code over GF(2) with n=312, k=11 and d=128.
This code was found by Heurico 1.16 in 0.0919 seconds.