The generator matrix

 1  0  1  1  1  6  1  1  8  1 14  1  1  0  1  1 14  1  1  1  4  1  1  4  1 10  1  1  0  1  1  1  1  1  1  6  1  4  2  6
 0  1 11  6  1  1  0 11  1  6  1 13  0  1  3  5  1  4 15  6  1 13  2  1  7  1 14  7  1  3 14  8  2  5  4  1  5  1  6  1
 0  0 12  0  0  0  0  0  0  8  8  4  4  4  8 12  4  4  4 12  4  8  0  0  4 12  0  4  4 12 12  8 12  4 12  4 12  4  4 12
 0  0  0 12  0  0 12  8  4  8 12  0  0  0 12 12 12  4  4  0 12  8 12 12  8  0  4  8 12  8  0  8  8  8  4 12  8  0 12 12
 0  0  0  0  4  0  0 12  8  0  8  0  4 12  4  8 12  4  0  4 12 12  0  8  8  4  8  0  0  4  0  4  8 12 12  8 12  0  0  0
 0  0  0  0  0  8  0  0  8  0  8  0  0  8  0  0  8  0  0  8  0  8  8  0  8  8  8  8  8  0  0  0  8  8  8  0  0  8  8  0
 0  0  0  0  0  0  8  8  0  8  8  8  0  8  8  0  8  0  8  0  0  0  8  8  8  0  0  0  8  8  8  8  0  8  0  8  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+231x^32+52x^33+540x^34+604x^35+2183x^36+4284x^37+7002x^38+12436x^39+10790x^40+12556x^41+7114x^42+4196x^43+2093x^44+644x^45+526x^46+44x^47+170x^48+50x^50+19x^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 33.7 seconds.