The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  8  1  0  2  4  1  1  1  2  1  8  1  1  2  0  2  1  8  1  1  8  1  2  1
 0  2  0  6  0  6  8  2  4  4  4  6 12 14  2 10  6  2 12  2  6  2  2  8 10  6 12  2 12 10 14  8 10  4  8  6 10  2  0 10  8
 0  0 12  0  0  0 12  0 12  4  8  4  0  4  4  4  0 12  4  4  8  4  8 12  4  4  4  8  8  0  8  4  4  4  4  8  4  0  8  4  8
 0  0  0 12  0  0  0  4  8  8  8  4  8  0  0 12  0  8 12  4  4 12  8 12  0  8 12  4  0  4  0  4 12  4  8  4  4  0  0  0 12
 0  0  0  0 12  0  4  8  0  4  8  0  4  0  8  0  8  8  0  0 12 12  4  4  4  4  8  8  8 12  4  8  8 12  8 12  4 12 12  4  8
 0  0  0  0  0  8  0  8  8  8  8  0  8  8  0  8  8  8  0  0  0  0  0  8  0  0  8  0  8  0  0  0  8  0  8  8  8  0  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+192x^34+84x^35+509x^36+684x^37+1271x^38+1628x^39+2689x^40+2324x^41+2589x^42+1772x^43+1346x^44+564x^45+385x^46+100x^47+137x^48+12x^49+75x^50+21x^52+1x^56

The gray image is a code over GF(2) with n=328, k=14 and d=136.
This code was found by Heurico 1.16 in 7.33 seconds.