The generator matrix

 1  0  0  1  1  1  6  1  2  1 12  1  4  1 10  1  1  6  1  6  1  1  4  0  1  2  1  2 12  1  1  6  8  1  2  1  1  4 10  1
 0  1  0  0  1 15  1 12  4 13  1  1  1  6  1  6  3  1  7 14 10 12  1  1 15 12  4  1  1  5  3  1  2  9 12  1 10  1  4  0
 0  0  1  1  1  4  1  4  1  8  1  3 14  3  6  9 15  7  4  1  0  6 11 13 10  1 14  4 15 14  7 10  1  5 14  1 13  5  1  0
 0  0  0  2  8 10 10 14  6 12  4 10  2  0  0  2  2  8 12 14  2  6  0 14  4 12  8  0 14 14 12 12 14 12  6 14  0  8  2  0

generates a code of length 40 over Z16 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+54x^34+624x^35+1363x^36+2858x^37+3632x^38+5066x^39+5593x^40+5330x^41+3670x^42+2580x^43+1075x^44+600x^45+196x^46+82x^47+30x^48+10x^49+2x^52+2x^53

The gray image is a code over GF(2) with n=320, k=15 and d=136.
This code was found by Heurico 1.16 in 6.5 seconds.