The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  4  2  0  2  1  1  1  1  1  2  2  2  2  2  1  1  1  2  1  2  0  1  1  2  2
 0  2  0  2  0  0 14  6  4  2  4 14 12  6 12  2  2  2 14  2  2  4  2 14  4  2 14 14  8 10  0  8 10  2  6 14 10 12  0  6  4 14
 0  0  2  2 12  6 14  0  4  6  2 12  0  2 14  4  6  6  0  4  2  6  8 14 12 14  4  6 10  8 10  8  2  8 12  6  6  2 10 10 12  0
 0  0  0  4  0  0 12  8  8 12  0  0  8  4  0  8  4 12  4  4  8  4  4  0 12  8  8 12  4  0  0  8  8 12  8  4  0 12  8  8  4  4
 0  0  0  0  8  0  0  0  8  0  0  0  8  8  8  8  0  8  8  0  8  0  0  0  8  0  8  0  0  8  8  0  0  8  0  8  8  0  0  8  8  8
 0  0  0  0  0  8  0  8  8  8  8  0  0  0  8  0  8  0  8  0  0  8  0  0  0  8  8  8  8  0  0  8  0  8  0  0  8  0  0  8  8  0
 0  0  0  0  0  0  8  0  0  0  8  8  8  0  0  0  8  8  8  0  8  0  0  0  8  8  8  0  8  0  8  8  8  0  0  8  8  0  8  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+77x^34+214x^35+479x^36+870x^37+1300x^38+2214x^39+3478x^40+4826x^41+5710x^42+5046x^43+3576x^44+2202x^45+1228x^46+794x^47+379x^48+150x^49+125x^50+52x^51+17x^52+16x^53+8x^54+6x^56

The gray image is a code over GF(2) with n=336, k=15 and d=136.
This code was found by Heurico 1.16 in 10.8 seconds.