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

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

Homogenous weight enumerator: w(x)=1x^0+24x^34+78x^35+139x^36+150x^37+248x^38+418x^39+714x^40+1436x^41+1836x^42+1430x^43+816x^44+348x^45+132x^46+118x^47+113x^48+76x^49+55x^50+36x^51+9x^52+6x^53+8x^54+1x^66

The gray image is a code over GF(2) with n=336, k=13 and d=136.
This code was found by Heurico 1.16 in 0.999 seconds.