The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+36x^34+218x^35+572x^36+1220x^37+2271x^38+3910x^39+5330x^40+5692x^41+5347x^42+4046x^43+2268x^44+1024x^45+441x^46+202x^47+77x^48+60x^49+29x^50+8x^51+8x^52+4x^53+4x^54

The gray image is a code over GF(2) with n=328, k=15 and d=136.
This code was found by Heurico 1.16 in 7.29 seconds.