The generator matrix

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

generates a code of length 40 over Z16 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+111x^34+12x^35+207x^36+92x^37+443x^38+664x^39+1124x^40+664x^41+382x^42+92x^43+144x^44+12x^45+80x^46+54x^48+7x^50+5x^52+1x^54+1x^64

The gray image is a code over GF(2) with n=320, k=12 and d=136.
This code was found by Heurico 1.16 in 0.343 seconds.