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

generates a code of length 42 over Z16 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+69x^28+115x^30+187x^32+270x^34+32x^35+307x^36+224x^37+399x^38+672x^39+424x^40+1120x^41+25040x^42+1120x^43+477x^44+672x^45+454x^46+224x^47+370x^48+32x^49+238x^50+161x^52+84x^54+40x^56+20x^58+10x^60+3x^62+2x^64+1x^70

The gray image is a code over GF(2) with n=336, k=15 and d=112.
This code was found by Heurico 1.16 in 14.9 seconds.