The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+172x^34+548x^35+1095x^36+1712x^37+3137x^38+4328x^39+7446x^40+8990x^41+10490x^42+8992x^43+7667x^44+4584x^45+3175x^46+1574x^47+845x^48+406x^49+232x^50+90x^51+32x^52+4x^53+10x^54+2x^55+2x^56+2x^59

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 38.5 seconds.