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

generates a code of length 64 over Z16 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+42x^56+52x^57+80x^58+78x^59+110x^60+352x^61+199x^62+1076x^63+228x^64+1068x^65+161x^66+328x^67+77x^68+44x^69+51x^70+44x^71+29x^72+16x^73+18x^74+10x^75+25x^76+4x^77+2x^78+1x^106

The gray image is a code over GF(2) with n=512, k=12 and d=224.
This code was found by Heurico 1.16 in 0.635 seconds.