The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  2  0  1  1  2  1  1 12  1  1  0  2  1  1  1  1  1  2  1  1  1  1  1  1  1  2  4  2  1  1
 0  2 12  6  0  6 12 10  0  6 12 10  6  2  0  6 10 10 12  2  0  0  2  6 12 12  6 10  0 10  0  6 14 10 12 10  8  6 12  0  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  0  0  0  8  8  8  8  8  8  0  8  0  8  0  0  8  8  0  8  8  8  0  8  0  0  0  0
 0  0  0  8  0  0  0  0  0  8  0  0  0  0  0  8  8  8  8  8  8  0  8  0  0  8  8  0  0  8  0  8  0  0  8  0  0  8  8  0  0  0
 0  0  0  0  8  0  0  0  0  0  8  0  0  8  8  8  0  8  0  0  8  0  8  8  8  8  8  8  0  8  0  0  0  0  8  8  0  0  0  0  0  0
 0  0  0  0  0  8  0  0  0  8  0  8  0  8  0  0  0  8  0  0  8  8  8  8  8  0  8  0  0  8  8  8  8  0  8  0  8  8  0  0  0  0
 0  0  0  0  0  0  8  0  0  0  0  0  8  8  8  0  8  0  8  0  8  8  0  0  8  0  8  0  0  8  0  0  8  8  8  0  8  8  8  8  0  0
 0  0  0  0  0  0  0  8  0  0  0  8  8  8  0  8  8  8  0  0  0  0  0  0  8  8  8  0  8  0  8  8  0  0  8  0  0  8  0  8  8  0
 0  0  0  0  0  0  0  0  8  0  8  8  8  0  8  0  0  8  0  8  0  8  0  8  8  0  8  8  0  0  8  0  8  8  0  0  8  8  8  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+51x^32+126x^34+8x^35+272x^36+152x^37+757x^38+520x^39+2237x^40+2392x^41+3369x^42+2392x^43+2234x^44+520x^45+746x^46+152x^47+279x^48+8x^49+104x^50+36x^52+17x^54+7x^56+1x^58+2x^60+1x^64

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 3.03 seconds.