The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+40x^56+56x^57+252x^58+140x^59+550x^60+368x^61+1065x^62+1010x^63+1348x^64+996x^65+1057x^66+336x^67+494x^68+86x^69+230x^70+36x^71+58x^72+18x^73+18x^74+8x^75+4x^76+10x^77+1x^78+2x^79+2x^81+1x^82+4x^83+1x^96

The gray image is a code over GF(2) with n=512, k=13 and d=224.
This code was found by Heurico 1.16 in 1.57 seconds.