The generator matrix

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

generates a code of length 42 over Z16 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+244x^34+56x^35+634x^36+512x^37+1700x^38+2040x^39+3993x^40+4556x^41+5314x^42+4540x^43+4055x^44+2104x^45+1640x^46+464x^47+564x^48+60x^49+198x^50+4x^51+63x^52+24x^54+2x^56

The gray image is a code over GF(2) with n=336, k=15 and d=136.
This code was found by Heurico 1.16 in 66 seconds.