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  1  1  2  1  1  1  1  1  2  1  1  1  2  1
 0  8  0  0  0  0  0  0  0  0  0  0  0  0  8  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  0  8  8  8  8  8  0  0  8  0  8  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  0  0  0  0  8  8  8  8  8  8  8  0  0  8  8  8  8  0  0  8  8  8  8  8  0  0  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  8  0  0  0  8  8  8  8  8  8  0  0  0  0  8  8  0  0  0  0  8  8  8  0  8  0  8  8  0
 0  0  0  0  8  0  0  0  0  0  0  0  0  8  0  8  8  8  8  8  8  0  8  8  0  8  8  8  8  8  8  8  8  8  8  8  8  8  8  0  8  0
 0  0  0  0  0  8  0  0  0  0  0  0  8  0  0  8  8  0  8  8  0  8  0  8  0  8  8  8  8  0  0  0  0  8  0  8  0  0  8  0  8  0
 0  0  0  0  0  0  8  0  0  0  0  0  8  0  0  0  8  8  8  8  0  8  8  0  8  0  8  0  0  0  8  0  0  8  8  0  0  8  8  0  0  0
 0  0  0  0  0  0  0  8  0  0  0  8  0  0  0  0  8  8  0  8  0  0  0  8  8  8  0  0  0  8  8  0  8  8  8  8  8  0  8  0  8  8
 0  0  0  0  0  0  0  0  8  0  0  8  0  0  0  8  0  0  8  0  8  0  0  8  0  0  0  0  8  8  8  8  0  8  8  0  8  0  8  0  0  8
 0  0  0  0  0  0  0  0  0  8  0  8  8  8  8  8  0  0  0  8  0  0  8  8  0  0  8  0  8  8  0  0  0  0  8  8  0  0  0  8  8  8
 0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  0  0  8  8  8  8  8  0  8  0  8  0  0  8  0  8  0  0  0  8  0  8  0  8  8  8  0

generates a code of length 42 over Z16 who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+67x^30+120x^32+138x^34+192x^36+187x^38+256x^39+193x^40+768x^41+12512x^42+768x^43+226x^44+256x^45+212x^46+175x^48+146x^50+92x^52+45x^54+23x^56+4x^58+2x^60+1x^78

The gray image is a code over GF(2) with n=336, k=14 and d=120.
This code was found by Heurico 1.16 in 4.6 seconds.