The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+152x^34+464x^35+1409x^36+2608x^37+4394x^38+7836x^39+9599x^40+12328x^41+9878x^42+8264x^43+4397x^44+2304x^45+1048x^46+428x^47+296x^48+72x^49+46x^50+10x^52+2x^54

The gray image is a code over GF(2) with n=328, k=16 and d=136.
This code was found by Heurico 1.16 in 26.7 seconds.