The generator matrix

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

generates a code of length 39 over Z16 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+58x^28+42x^29+115x^30+170x^31+235x^32+364x^33+620x^34+1634x^35+1246x^36+4686x^37+1819x^38+10708x^39+1833x^40+4776x^41+1256x^42+1684x^43+611x^44+326x^45+241x^46+130x^47+82x^48+44x^49+44x^50+10x^51+20x^52+2x^53+1x^54+9x^56+1x^60

The gray image is a code over GF(2) with n=312, k=15 and d=112.
This code was found by Heurico 1.16 in 12.3 seconds.