The generator matrix

 1  0  1  1  1  6  1 12  1  1 14  1  2  1  1  1  8  1  1 14  1 10  8  1  1  4  0  1  1  1  1  1  1  8  1  1  4  1  2  1  1
 0  1 11  6 13  1  8  1 11 13  1  2  1  3  6  4  1  5 15  1  6  1  1  1  2  1  1 10  8  8  9 14  3  4  3  0  2  2  0  0  0
 0  0 12  0  4  0  0  8  8  0  8  0  0  0  4 12  4  4  4 12  8  4  8 12  4 12  4  0 12  0  4 12  8 12  0  0  8  8  8 12  4
 0  0  0 12  0  0  4  8 12  4 12  4 12  0  4  8  8 12  4  0  0 12 12  8  8  0  4  8  8 12 12  4  8  4  4  8  4 12  4 12  4
 0  0  0  0  8  0  8  8  8  0  8  8  0  8  8  8  0  0  8  8  0  0  0  0  8  8  8  8  8  0  8  0  8  8  8  0  8  0  0  0  0
 0  0  0  0  0  8  0  8  0  0  0  8  8  0  8  8  0  8  0  8  8  0  0  8  0  0  8  8  0  0  8  8  8  8  8  8  0  8  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+22x^34+156x^35+261x^36+612x^37+1224x^38+1876x^39+2857x^40+2430x^41+2874x^42+1848x^43+1196x^44+628x^45+210x^46+78x^47+29x^48+38x^49+16x^50+8x^51+7x^52+4x^53+6x^54+2x^55+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 1.98 seconds.