The generator matrix

 1  0  0  1  1  1  6  1  1 14 12  6  1  1  0 14  4  1  1 14  1  1  1 10  4  1  1  6  1  1  0  2  0  0  2  1 10  1  8  1  1
 0  1  0  2  1 11  1 14  0  4  1  1  9 15  6  2  1  8  5  1  6  7  8  1  8 15  3  1  1 11  1  4  1  1  1  2  2  9  1  4  0
 0  0  1  1  5  4  1  3  6  1  6  7  7  6  1  1  1  7  4  6  4  7  5  5  1  9  4 14 13  5  4  1 11  1  0  4  1  0  9  6  0
 0  0  0  4  4  0 12  4  0  0  8  4 12  8  8  0  0  8  4  4  4  8  4  0 12  4 12  0  8  8 12  4  8  4  4  8 12  0 12  4  0
 0  0  0  0  8  0  8  8  8  8  8  0  8  0  8  0  8  8  0  8  8  8  0  8  0  8  8  8  0  0  8  0  0  0  0  0  0  8  0  0  0
 0  0  0  0  0  8  0  8  8  8  0  0  8  0  0  8  8  0  8  8  0  8  0  0  8  8  8  8  0  8  0  8  0  8  0  0  8  0  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+103x^34+348x^35+1375x^36+2064x^37+5411x^38+7212x^39+10912x^40+10562x^41+11280x^42+7104x^43+5362x^44+1998x^45+1229x^46+364x^47+131x^48+30x^49+24x^50+12x^51+11x^52+2x^53+1x^58

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 21.5 seconds.