The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  0  1  1  1  1  1  1  2  1 12  1  1  1  1  1  2  1  1  1  0  2  1  1 12  1  1  2  1  1  1  2  1  2  0  0  1  2  2  4
 0  2 12  6  0  6 12 10  0  6 12 10 10  4  6  0  8 14 12 10  6  6  0 12 10  2 14 12 10  0 10  8 10 12  2 12  4  6  4 14  6  4  0  0  2 10 12 10  2  2  6  6 14 12  2 10  2  6  2  2 12 10  6  8
 0  0  8  0  0  0  0  0  0  0  8  0  0  0  0  8  8  0  8  8  8  8  8  8  8  0  8  0  0  8  8  0  0  0  0  8  8  0  8  8  0  8  0  0  8  0  8  8  8  8  0  0  0  8  0  8  8  8  8  0  0  8  0  8
 0  0  0  8  0  0  0  0  0  8  8  0  0  8  8  8  8  8  8  8  0  8  0  0  8  8  0  0  8  0  0  0  0  8  0  8  8  0  0  0  8  8  8  0  8  8  0  8  8  0  0  0  8  8  0  0  0  0  0  0  8  8  8  8
 0  0  0  0  8  0  0  0  8  0  0  8  8  0  8  0  8  8  0  8  8  0  0  0  8  0  0  0  0  0  8  8  0  8  8  8  8  0  8  8  0  0  8  0  8  0  8  8  0  8  8  0  8  0  8  0  8  0  0  8  8  8  8  0
 0  0  0  0  0  8  0  0  0  8  0  8  8  0  0  8  8  8  8  8  0  0  8  0  8  0  0  8  0  8  8  0  0  0  8  0  8  0  8  0  8  0  8  8  8  8  0  0  0  8  0  8  0  8  0  0  8  0  0  0  8  0  0  8
 0  0  0  0  0  0  8  0  8  0  8  0  0  0  8  0  0  8  8  8  8  8  0  8  0  8  8  0  8  0  0  8  8  0  0  0  8  8  0  8  8  8  0  0  0  0  0  0  0  8  8  0  0  0  8  8  8  8  0  0  8  8  0  8
 0  0  0  0  0  0  0  8  0  0  8  8  0  8  8  8  8  8  0  0  8  0  0  8  8  8  0  0  0  8  0  8  0  0  8  0  0  8  0  0  0  0  0  8  8  8  8  0  8  8  0  0  8  0  8  8  0  0  8  8  0  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+97x^56+28x^57+245x^58+168x^59+474x^60+440x^61+1170x^62+664x^63+1696x^64+640x^65+1158x^66+408x^67+466x^68+168x^69+214x^70+40x^71+71x^72+4x^73+19x^74+4x^76+8x^78+6x^80+2x^82+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 1.62 seconds.