The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  2  2  4  1  1  4  1  8  1  4  4  1  2
 0 12  0  0  0  4 12  4  8  0  4  0  8  4  4  4  4  0 12  0  4  0  4  8  4  4 12 12 12  4  4 12  4  8  8  4 12  4  8  0  0
 0  0 12  0  4  4 12  0  0  4  8  0 12 12  8  4  4  0  8  4  0  4  0  8  4  8 12  8  8 12 12  0 12 12  0  4  0  0  4  0 12
 0  0  0 12  4  0 12  4  4  8  0  8  4  4  4  8  8  0 12  4  0  4  8  0 12 12  4  8  8  8  8 12  4 12  8  8  8 12  0  8  8
 0  0  0  0  8  0  0  8  0  8  8  0  0  0  0  8  0  0  8  0  8  0  8  8  0  0  8  8  8  8  8  0  8  0  8  0  8  0  8  8  0
 0  0  0  0  0  8  0  8  8  8  0  8  8  0  8  8  0  8  8  0  8  0  0  8  8  8  8  8  0  0  0  0  8  8  0  8  8  0  8  0  8
 0  0  0  0  0  0  8  0  8  8  8  0  0  0  0  0  0  8  8  8  8  0  0  8  0  8  8  0  0  8  0  8  8  0  0  0  8  8  0  8  8

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

Homogenous weight enumerator: w(x)=1x^0+157x^34+12x^35+336x^36+120x^37+657x^38+756x^39+1449x^40+1296x^41+1447x^42+756x^43+612x^44+120x^45+243x^46+12x^47+146x^48+48x^50+15x^52+8x^54+1x^60

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 1.25 seconds.