The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  0  0  4  8  1  1  0  8  2  2  4  1  2  1  1  4  2  1  4  1  4  1  1
 0  2  0  0  0  2 14  2  4  4  6  4 14  8  2 14  8  2  0  0  2  2  4  6 12  2  2  6 10  2  2 10 14  4  2  4  8  0  2  2  0  8
 0  0  2  0  2  2  2  8 10  4  0  0  0  6 14  2  2 12  4  4  2  0  2 10  4  6  8 10  0 12 12  4 14  8  6 10  8 12  0  8 12 14
 0  0  0  2  2  0 10  2  8 12  4 10 10 10  0 14  6  0 12  2  8 10  2 14  6  6  0 12 12  2  0  4  4 12 12 12  0  2 14  4 12 10
 0  0  0  0  4  0  4  0  0 12  4  4 12  8  4  0  8  8 12  4 12  8 12  4 12  0 12  0 12  4  4 12  8 12 12  0 12  8  8  8  8 12
 0  0  0  0  0  8  0  0  8  8  8  8  8  8  0  8  8  0  8  8  0  8  8  8  0  0  8  0  0  0  0  0  0  8  8  0  0  0  8  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+153x^34+400x^35+994x^36+1618x^37+3024x^38+4204x^39+7687x^40+8582x^41+11937x^42+8672x^43+8150x^44+4346x^45+2807x^46+1456x^47+827x^48+354x^49+212x^50+48x^51+36x^52+12x^53+9x^54+4x^55+1x^56+2x^58

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 39.4 seconds.