The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  1  0  6  1  1 12  1  1  1  0 10  1  1  1  1  6  1  1  1 10  1  1  0  0 12  0  1
 0  1  3  6  5  1 12  7  1 10  9  1  0  3  1  1  6  5  1 12 15 10  1  1  9  6  5  0  1  3 10 15  1  9 12  1  1  1  1  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  8  0  8  8  8  8  8  0  8  8  8  8  8  0  0  0  0  0
 0  0  0  8  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  0  0  8  8  8  8  0  0  0  8  0  0  0  0  8  0  0  8  0  0  0
 0  0  0  0  8  0  0  0  0  8  8  8  0  8  8  8  0  0  8  8  0  0  0  8  0  0  0  8  8  0  8  0  0  8  8  8  0  0  8  0
 0  0  0  0  0  8  0  0  8  8  0  8  0  0  8  0  8  8  8  0  8  8  0  8  0  0  8  0  8  0  8  8  0  0  8  8  8  0  0  0
 0  0  0  0  0  0  8  0  8  0  0  8  8  0  0  8  8  0  8  8  0  0  0  0  8  0  8  0  8  0  0  8  8  8  0  8  0  8  0  0
 0  0  0  0  0  0  0  8  8  8  8  0  0  0  0  8  8  8  8  0  0  0  8  8  0  8  8  8  0  0  8  0  8  0  0  0  8  0  0  8

generates a code of length 40 over Z16 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+16x^32+50x^33+98x^34+110x^35+440x^36+1514x^37+1067x^38+4214x^39+1403x^40+4214x^41+1046x^42+1514x^43+419x^44+110x^45+80x^46+50x^47+17x^48+8x^50+4x^52+5x^54+3x^56+1x^60

The gray image is a code over GF(2) with n=320, k=14 and d=128.
This code was found by Heurico 1.16 in 1.78 seconds.