The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+54x^32+58x^33+113x^34+158x^35+281x^36+432x^37+924x^38+1404x^39+1404x^40+1404x^41+892x^42+432x^43+252x^44+144x^45+87x^46+52x^47+53x^48+10x^49+27x^50+2x^51+3x^52+4x^54+1x^62

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 0.932 seconds.