The generator matrix

 1  0  1  1  1  6  1  1  8  1  1 14  1  4  1  1  1  0 14  1  1  0  1  1  2  1  0 14  1  1  4  1 10 12  1 14  1  1  1  1
 0  1 11  6  1  1  8 11  1 13  6  1 10  1  3 13  8  1  1 15  0  1 14  5  1  1  1  1 14 15  1  2  1  2  7  1 14  4  3  0
 0  0 12  0  0  0  0  0  8  4  4  4  4  8  0  4  8  0  8 12  4 12  8 12  4 12  4  0 12 12 12 12  8  0  8 12 12  0  4  0
 0  0  0 12  0  0 12  8 12  0  0 12  0  4  8 12  0 12  8  0  4 12  8  4 12 12  0  8  0 12  8 12 12 12  8  0  0  4 12  0
 0  0  0  0  4  0  8  4  0  8  4 12 12  0  8  4  4  4  4 12  8  0 12  8 12  4 12 12  0  0  8 12  4  0  4  8  0  0  8  0
 0  0  0  0  0  8  8  8  0  8  8  8  0  8  8  0  8  0  8  8  0  0  0  0  0  8  0  0  8  8  0  8  8  8  8  8  0  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+57x^32+98x^33+171x^34+604x^35+899x^36+2418x^37+3645x^38+5598x^39+5756x^40+5588x^41+3810x^42+2420x^43+786x^44+572x^45+158x^46+80x^47+50x^48+26x^49+19x^50+3x^52+2x^53+5x^54+2x^55

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 7.23 seconds.