The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 12  1  2  1  2  8 12  1  1 12  2  2 12  1  1 12  4  1  1  1  2  1  2  1
 0  2  0  0  0  2 14  2  4  2  4 14 10  8  6  6  2  8  0 12 10  2  4 10  8  2  8 10  8 12  0  8  2  2 14  2  6 10 10  0
 0  0  2  0  2  2  2  8 14  6 12  0 12  6 10  6  4 10  2  8  0  2  2  8  6  6 12  2  2  0  4  0 14 10  6  6  4  4  6  8
 0  0  0  2  2  0 10  2  0  8  8  0 14  2 10 12 10 12  6 10 12  2  4  4  6  0 14 14 14 14  4  2  8  0  2  0  2 12  2  0
 0  0  0  0  4  0  4  0 12 12  4 12  4  8  8  8  0  0 12 12 12 12  8  8 12  0  8  4  8  8  0  0  4 12  8  8  8  8 12  8
 0  0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  0  8  8  8  0  8  8  0  0  8  8  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+108x^32+420x^33+851x^34+1482x^35+2637x^36+4350x^37+7204x^38+10060x^39+11007x^40+10156x^41+7608x^42+4572x^43+2465x^44+1334x^45+669x^46+326x^47+164x^48+60x^49+49x^50+6x^51+2x^52+2x^54+2x^55+1x^62

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 36.9 seconds.