The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  2  0  1  1  1  1  1  1  8  1  2  1  1  1  4  2  1  1  2  1  1  4  0  1  1  1
 0  2  0  6  4  6 12  2  8  6  0  6  4 14  2  6  2  4 14  8 10  0 10  2  2 14  0  4  6 12 10 12  4  6 10 12  2  0 12 14  0
 0  0 12  0  4  0  0  0  8  4  4 12  8  0  4  0  8 12  0  4  4 12  4 12  8  8  0  4 12 12  0  4 12  8  8  8 12  4  0  4  0
 0  0  0 12  0  0  8 12 12 12 12  8  4  0  4  0  8 12 12  8  8  4  8  8  8  4  8  8 12 12  8 12 12  0  4 12  8  8  4  0  0
 0  0  0  0  8  0  8  8  0  8  0  0  8  8  8  8  0  8  0  0  8  8  0  0  8  8  8  8  0  0  0  0  0  0  8  8  8  8  0  0  0
 0  0  0  0  0  8  0  0  0  8  0  8  0  0  0  8  8  0  8  8  0  8  0  0  8  8  8  8  8  0  0  0  8  0  8  8  0  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+40x^34+98x^35+215x^36+342x^37+657x^38+666x^39+1661x^40+894x^41+1665x^42+680x^43+647x^44+268x^45+150x^46+82x^47+58x^48+30x^49+15x^50+10x^51+10x^52+2x^53+1x^62

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 0.785 seconds.