The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+257x^34+408x^35+946x^36+1488x^37+3047x^38+4744x^39+6736x^40+9488x^41+10774x^42+10112x^43+6930x^44+4824x^45+2872x^46+1320x^47+871x^48+320x^49+256x^50+56x^51+68x^52+8x^53+9x^54+1x^66

The gray image is a code over GF(2) with n=336, k=16 and d=136.
This code was found by Heurico 1.16 in 39 seconds.