The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+34x^34+72x^35+194x^36+380x^37+729x^38+832x^39+1360x^40+1068x^41+1372x^42+808x^43+702x^44+326x^45+155x^46+56x^47+28x^48+32x^49+12x^50+8x^51+18x^52+2x^53+2x^54+1x^56

The gray image is a code over GF(2) with n=328, k=13 and d=136.
This code was found by Heurico 1.16 in 0.773 seconds.