The generator matrix

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

generates a code of length 42 over Z16 who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+86x^35+260x^36+376x^37+548x^38+1106x^39+1641x^40+3074x^41+2295x^42+3034x^43+1666x^44+1070x^45+496x^46+366x^47+197x^48+78x^49+47x^50+16x^51+10x^52+10x^53+4x^54+1x^56+1x^58+1x^66

The gray image is a code over GF(2) with n=336, k=14 and d=140.
This code was found by Heurico 1.16 in 26.4 seconds.