The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  0  1  1  6  1  1 12  1 10  1  0  1  1  0  1  1  1  1  1  6  1  1  1  6  1  1  1  1
 0  1  3  6  5  1 12  7  1 10  9  1  1  0  5  1  6  3  1 15  1 12  1  9 10  1  0  3  6  5 12  1 10  9  6  1  5  6  5  5
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  0  0  0  8  8  8  8  8  8  0  8  8  0  0  8  8  8  8  0  0  8  8  0  8  8
 0  0  0  8  0  0  0  0  0  0  0  0  0  8  0  8  0  8  0  0  8  8  8  8  8  8  0  0  8  8  0  0  0  8  8  0  8  8  8  8
 0  0  0  0  8  0  0  0  0  0  0  8  8  0  8  8  8  8  8  0  0  0  0  8  0  8  8  8  8  0  0  0  8  0  0  0  8  0  8  0
 0  0  0  0  0  8  0  0  0  0  8  8  8  0  8  0  0  8  8  8  0  8  8  0  0  0  0  0  0  8  8  0  0  8  8  8  0  8  0  0
 0  0  0  0  0  0  8  0  0  8  8  0  0  8  8  0  0  8  8  0  8  0  0  8  0  0  8  8  0  8  0  0  8  8  0  0  0  0  8  8
 0  0  0  0  0  0  0  8  0  8  0  0  0  0  0  0  8  8  0  8  0  8  0  8  8  0  8  8  8  0  0  8  0  8  8  8  0  0  0  8
 0  0  0  0  0  0  0  0  8  0  8  8  0  0  8  8  8  8  0  8  8  0  8  8  8  0  8  0  0  0  8  8  0  8  0  0  0  0  8  8

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

Homogenous weight enumerator: w(x)=1x^0+125x^32+24x^33+224x^34+168x^35+1180x^36+1912x^37+4256x^38+5064x^39+6891x^40+5064x^41+4256x^42+1912x^43+1149x^44+168x^45+224x^46+24x^47+96x^48+22x^52+7x^56+1x^60

The gray image is a code over GF(2) with n=320, k=15 and d=128.
This code was found by Heurico 1.16 in 6.93 seconds.