The generator matrix

 1  0  1  1  1  4  1  1  2  1 14  1  1  6  1  1 12  1  1  4  1  1 12  4  1 12  1  8  2  1  0  1  1  1 12  1  6  1  1  6  4  1
 0  1  1  0 11  1 14 15  1  2  1  5 11  1  7  0  1 10 13  1 14 13  1  2 13  1  6  1 14  2  1 11 14  0  0 11  1 15  1  1  4  0
 0  0  2  6  0  2  8  2  6  2  0  4  4 12 10  6  6  0  8 14  0 12  4  2  2  0  4  4 10  6  0 14  2  4  2  6  8 10  4  2  0  0
 0  0  0 12  0  4  0  0 12  4  8 12  4 12 12  8  8  4  8  8 12  8  0  8  0 12  8  4 12  4  8  0  0  0 12 12  0  4  4  0  0  0
 0  0  0  0 12  4  4  4  0  4 12  8 12  0 12  8  0  4 12  4  0  8  4  0  0  4 12  4 12  8  4  4 12  8  4  0  8  0  0 12  4  8
 0  0  0  0  0  8  0  0  8  0  0  0  0  0  0  0  8  0  8  8  0  8  8  0  8  0  8  8  8  8  8  0  8  8  0  8  8  0  0  8  8  8

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

Homogenous weight enumerator: w(x)=1x^0+56x^34+258x^35+567x^36+1362x^37+2551x^38+4908x^39+6840x^40+10846x^41+10582x^42+10948x^43+7204x^44+4972x^45+2260x^46+1244x^47+523x^48+216x^49+98x^50+50x^51+29x^52+10x^53+5x^54+4x^56+2x^57

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 27.7 seconds.