The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  1  0  6  1  1 12  1  1 10  1  0  1  1  1  1  6  1  1  1  1 12  1  0  1 12  6  1  0  1
 0  1  3  6  5  1 12  7  1 10  9  1  0  3  1  1  6  5  1 12 15  1 10  1  9  6  5  0  1  3 10 15  9  1  6  1  3  1  1  3  1  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  0  8  8  8  8  8  8  0  8  8  8  0  0  8  8  0  0  0  0  0
 0  0  0  8  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  0  0  8  8  8  8  0  0  0  8  0  0  0  8  8  0  8  8  0  0  0  8  0
 0  0  0  0  8  0  0  0  0  8  8  8  0  8  8  8  0  0  8  8  0  8  0  0  0  0  0  8  8  0  8  0  8  0  0  8  0  8  0  8  8  0
 0  0  0  0  0  8  0  0  8  8  0  8  0  0  8  0  8  8  8  0  8  8  8  0  0  0  8  0  8  0  8  8  0  8  0  8  8  0  8  8  0  0
 0  0  0  0  0  0  8  0  8  0  0  8  8  0  0  8  8  0  8  8  0  0  0  0  8  0  8  0  8  0  0  8  8  8  8  0  8  0  8  0  0  0
 0  0  0  0  0  0  0  8  8  8  8  0  0  0  0  8  8  8  8  0  0  8  0  8  0  8  8  8  0  0  8  0  0  0  8  8  0  0  0  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+17x^34+34x^35+118x^36+198x^37+512x^38+1090x^39+2069x^40+2518x^41+3311x^42+2518x^43+2046x^44+1090x^45+490x^46+198x^47+103x^48+34x^49+15x^50+10x^52+4x^54+3x^56+1x^58+2x^60+2x^62

The gray image is a code over GF(2) with n=336, k=14 and d=136.
This code was found by Heurico 1.16 in 1.93 seconds.