The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+25x^34+104x^35+338x^36+564x^37+1229x^38+1744x^39+2808x^40+2896x^41+2696x^42+1772x^43+1266x^44+450x^45+280x^46+114x^47+31x^48+20x^49+23x^50+8x^51+4x^52+6x^53+3x^54+2x^55

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 1.95 seconds.