The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+43x^34+8x^35+398x^36+104x^37+693x^38+400x^39+896x^40+400x^41+602x^42+104x^43+336x^44+8x^45+66x^46+29x^48+3x^50+2x^52+1x^54+2x^56

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 0.239 seconds.