The generator matrix

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

generates a code of length 41 over Z16 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+70x^34+624x^35+2303x^36+5072x^37+9874x^38+14800x^39+20879x^40+23144x^41+21810x^42+15216x^43+9611x^44+4696x^45+2034x^46+616x^47+204x^48+80x^49+18x^50+8x^51+10x^52+2x^58

The gray image is a code over GF(2) with n=328, k=17 and d=136.
This code was found by Heurico 1.16 in 84.1 seconds.