The generator matrix

 1  0  1  1  1  6  1  1  0  1 14  1  1  1 14  1  1  6  1  1  8  1  1  1  6  1  1  0  1  1  1  2  4  1  2  1  1  1  0  2
 0  1 11  6  1  1  8  5  1 10  1  3  5  8  1  6 11  1 13  4  1  8  9  3  1  5 11  1 14  0  3  1  1  1  2  2 10 11  1  0
 0  0 12  0  0  0  0  0  0  0  0  4  4  4  4 12  4  4  8  4  4 12  0  8  8  4  4  4 12 12  8  0 12  4  8  4  8  8 12  8
 0  0  0 12  0  0  0  0  4 12 12  8  4  8  0 12 12  8  4  0 12  4  8 12  8  4  8  8  4  4  4 12 12  0  8  4 12  8  4  0
 0  0  0  0  4  0  8  4  0  8  0  8  8 12  4 12  0  4  4 12 12  4 12  4  4 12  4  8  0  8  0 12  4  0  4  0  8  8 12 12
 0  0  0  0  0 12 12  4 12  4  8  4  0 12 12 12  4  0 12  4  0  8  4  0 12  4 12  4  4  8  0 12  8  0  8  4 12 12  4 12

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

Homogenous weight enumerator: w(x)=1x^0+224x^32+68x^33+606x^34+740x^35+2058x^36+3944x^37+8090x^38+10680x^39+12938x^40+10420x^41+7946x^42+4116x^43+2233x^44+672x^45+454x^46+80x^47+189x^48+56x^50+20x^52+1x^60

The gray image is a code over GF(2) with n=320, k=16 and d=128.
This code was found by Heurico 1.16 in 28.3 seconds.