The generator matrix

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

generates a code of length 42 over Z16 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+114x^32+68x^34+32x^35+426x^36+96x^37+400x^38+1312x^39+1775x^40+2656x^41+2648x^42+2656x^43+1776x^44+1312x^45+400x^46+96x^47+389x^48+32x^49+68x^50+98x^52+25x^56+4x^60

The gray image is a code over GF(2) with n=336, k=14 and d=128.
This code was found by Heurico 1.16 in 4.31 seconds.