The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  1  2  2  4  4  1  4  1  1  1  2  4  4  1  4  1  1
 0 12  0  0  0  4 12  4  8  0  4  0  8  4  4  4  4  0 12  0  4  8 12  0  0  8  8 12  4  4  8  0 12  8  8  0  8 12 12  0
 0  0 12  0  4  4 12  0  0  4  8  0 12 12  8  4  4  0  8  4  0  4 12  4  8 12  4  0  4  8  0  8  8  8  0 12  0  8  4  0
 0  0  0 12  4  0 12  4  4  8  0  8  4  4  4  8  8  0 12  4  0  0  4  4  4  4  0  8  0 12  0  8 12  4  4  8 12  0  4  0
 0  0  0  0  8  0  0  8  0  8  8  0  0  0  0  8  0  0  8  0  8  8  8  0  8  8  0  0  8  0  8  0  8  8  8  8  0  8  0  0
 0  0  0  0  0  8  0  8  8  8  0  8  8  0  8  8  0  8  8  0  8  0  8  0  0  0  0  0  0  8  8  0  0  8  0  8  0  8  8  0
 0  0  0  0  0  0  8  0  8  8  8  0  0  0  0  0  0  8  8  8  8  0  8  0  0  8  0  8  8  8  0  8  0  0  8  0  8  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+58x^32+76x^33+144x^34+156x^35+253x^36+694x^37+750x^38+1128x^39+1713x^40+1122x^41+746x^42+708x^43+233x^44+138x^45+121x^46+48x^47+40x^48+18x^49+25x^50+8x^51+6x^52+5x^54+1x^58

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 0.907 seconds.