The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  1  4  2  8  4  2  2  2  1  4  2
 0 12  0  0  0  0  0  0  0  0  8  4 12 12  8 12  4  4  4  8  0 12  0 12  4  0  4 12  8 12  0  0  8  8  0  8 12  8  4  4  4  0
 0  0 12  0  0  0  0  0  0  0 12  8  4 12  4  4  0  4  8  8 12  0  8  8  4 12 12  8  0  0  8  4  8  4  4  0 12  4 12  4  8  8
 0  0  0 12  0  0  8 12 12  4  4 12  8 12 12  8  4 12 12  0  4  0  4  0  0 12 12  4 12  4  4  8  8  0  4  4  8  4 12  0  8  4
 0  0  0  0 12  0 12 12  4  8  0  0  0  0  8 12  0 12  4  8 12  8  0  4  4  4  8  4  4 12  8 12  8  8  4  0  4  0 12 12  8  4
 0  0  0  0  0 12  4  8  4  4  0  0  0  0  4  0  4 12  8  8 12  0  8 12 12  0  4 12  8  0  8 12 12  0  4  8  0 12  8  8  4 12

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

Homogenous weight enumerator: w(x)=1x^0+206x^34+4x^35+495x^36+92x^37+710x^38+600x^39+1968x^40+2368x^41+3520x^42+2388x^43+1989x^44+604x^45+716x^46+80x^47+355x^48+8x^49+202x^50+51x^52+22x^54+4x^56+1x^60

The gray image is a code over GF(2) with n=336, k=14 and d=136.
This code was found by Heurico 1.16 in 4.42 seconds.