The generator matrix

 1  0  1  1  1  6  1  1  8  1  1 14  1  4  1  1  1  6  1  1  8  1  1 12  8  1  1  1  4  1  0  2  1  2  2  1  1  2  1  2  6  1
 0  1 11  6  1  1  8 11  1 13  6  1 10  1 11  1  0  1  5  2  1  8  3  1  1  2  5 14  1  9  1  1  7  8  4 12  9  1 14 14  1  0
 0  0 12  0  0  0  0  0  8  4  4  4  4  8  4  8  0  0 12 12  8 12  4  8  4  4  0  8 12  8  4  0  0 12  0 12 12  8  4  4 12  0
 0  0  0 12  0  0 12  8 12  0  0 12  0  4  4 12  4 12  8  0  8  8  0  4  8 12  0  0  8 12  4 12 12 12  8 12 12  8  0  0  8  0
 0  0  0  0  4  0  8  4  0  8  4 12 12  0  4  8  4  4 12  8 12  0  4  4  8 12  8  4  0 12  8  0  0 12  4 12  8 12  0  8  4  0
 0  0  0  0  0  8  8  8  0  8  8  8  0  8  0  0  0  8  8  8  8  0  0  0  0  8  8  8  8  8  8  8  8  8  8  0  8  8  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+49x^34+110x^35+291x^36+568x^37+1312x^38+2082x^39+3972x^40+4884x^41+6117x^42+5008x^43+4176x^44+2110x^45+1097x^46+442x^47+301x^48+112x^49+58x^50+38x^51+25x^52+6x^53+7x^54+2x^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 7.79 seconds.