The generator matrix

 1  0  1  1  1  4  1 14  1  2  1  1 14  1  1 10  1  1 12  1  1  1  2  4  1  0  4  2  1  8  1  1  1 12  4  1  4 12  1  1
 0  1  1  0 11  1 14  1 15  1  5  2  1 15  8  1 11  6  1  2  8  5 10  1  9  1  4  0  1 12  1  8 12  1  1  2  0  1  8  0
 0  0  2  6  0  2  8  0 10  6  0  2  4 14  4 10  4 14  2 14  0  4  6 10  8  8  2  6 14  2 14  2  4  0  2  2  2  0  0  0
 0  0  0 12  0  4  0  0 12  4  8 12  0  4  8  4  4  8  0  8  4  4  0  8  4  4  0 12  4  4  0  8  4  4  0  0  0  8  4  0
 0  0  0  0 12  4  4 12  8  0  8 12  8 12  8  8 12  0  4  4  8  8  0  8 12  8  8  4  8  4 12  0 12  4  0 12  4  4  8  8
 0  0  0  0  0  8  0  8  8  8  0  0  8  0  8  0  8  8  8  0  8  0  8  8  0  0  0  8  0  0  8  0  0  0  8  8  8  8  0  8

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

Homogenous weight enumerator: w(x)=1x^0+53x^32+196x^33+597x^34+1132x^35+2422x^36+4366x^37+7789x^38+10070x^39+12011x^40+10468x^41+7941x^42+4234x^43+2373x^44+1024x^45+483x^46+202x^47+95x^48+40x^49+22x^50+10x^51+5x^52+2x^53

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 25.8 seconds.