The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  4  1  1  1  2  2  1  4  1
 0 12  0  0  0  0  0  0  0 12  4 12 12  8  8  0 12 12  4 12  4  8 12 12  8 12  4  0  8 12  4  0  0  4  4  4  4  0  8  8
 0  0 12  0  0  0  4 12  4  4  4  8  0  8 12  8  0  0  8  4 12  4  4  8  4  8  0  4  0  0  0  0  8 12  4  4  0  8  8  8
 0  0  0 12  0  4  4  4  8  4  0 12  4  8  8  0  4  8  8  0 12  0  8 12 12  8 12  0 12 12  0 12 12  4  0  0 12  0  4 12
 0  0  0  0 12  4  0  4  4  8  0  8 12  0  8 12  8  8  4  0  8  8  4  4 12  4  4  4 12  4 12  0  4  4  8  8  0  4 12  0
 0  0  0  0  0  8  0  0  8  0  8  8  8  8  8  8  0  8  8  8  8  0  8  8  8  0  0  8  8  8  0  0  0  8  8  0  8  8  8  8
 0  0  0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  8  8  0  8  0  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+200x^32+424x^34+8x^35+593x^36+232x^37+1586x^38+2832x^39+4640x^40+2832x^41+1620x^42+232x^43+590x^44+8x^45+356x^46+175x^48+44x^50+8x^52+2x^54+1x^68

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 4.12 seconds.