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

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

Homogenous weight enumerator: w(x)=1x^0+218x^34+438x^36+8x^37+614x^38+168x^39+1104x^40+2896x^41+5516x^42+2896x^43+1113x^44+168x^45+623x^46+8x^47+368x^48+181x^50+45x^52+15x^54+2x^56+1x^58+1x^72

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 92.4 seconds.