The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  1  1  1  2  1  4  0  1  2  1  1  1  1  4  4  4  2  1  1
 0 12  0 12  0 12  0 12  8  4  0 12  0 12  8  4  0  0  0  8  0 12 12 12  4 12 12  4 12  4 12 12  8  4  0  8 12 12  0  8 12 12
 0  0  8  0  0  0  0  0  8  0  0  0  8  8  8  8  0  0  8  8  8  0  8  0  8  8  8  8  0  8  0  8  0  0  0  8  8  0  0  0  8  8
 0  0  0  8  0  0  0  0  0  8  0  8  8  8  8  0  0  8  8  8  0  0  0  0  8  0  0  8  0  8  8  0  0  8  0  0  8  8  8  0  8  8
 0  0  0  0  8  0  0  0  0  0  8  0  8  0  8  0  0  8  8  0  0  0  8  8  8  8  0  8  8  8  0  8  0  8  8  8  0  0  8  8  8  0
 0  0  0  0  0  8  0  0  0  0  0  8  0  8  0  8  8  8  8  8  8  0  8  8  0  8  0  0  0  8  8  0  8  0  0  0  8  8  0  0  0  0
 0  0  0  0  0  0  8  0  8  0  8  8  8  0  0  8  8  8  8  0  8  8  0  8  0  0  0  8  8  0  8  8  0  0  0  0  0  0  8  8  8  8
 0  0  0  0  0  0  0  8  0  8  8  8  0  0  8  8  0  0  8  8  8  8  8  0  0  0  0  8  0  0  0  8  8  0  8  0  8  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+30x^34+130x^36+32x^37+114x^38+288x^39+182x^40+1216x^41+120x^42+1216x^43+216x^44+288x^45+78x^46+32x^47+96x^48+32x^50+12x^52+8x^54+2x^58+2x^60+1x^64

The gray image is a code over GF(2) with n=336, k=12 and d=136.
This code was found by Heurico 1.16 in 0.358 seconds.