The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+133x^32+98x^34+32x^35+414x^36+416x^37+512x^38+2112x^39+772x^40+2112x^41+548x^42+416x^43+358x^44+32x^45+112x^46+82x^48+10x^50+26x^52+4x^56+2x^60

The gray image is a code over GF(2) with n=320, k=13 and d=128.
This code was found by Heurico 1.16 in 3.9 seconds.