The generator matrix

 1  0  1  1  1  4  1  8  1  1 12  1  1 10  1 10  1  1 10  1  1  1  4  1  1  1 10  8  1  1  2  1  1  6  1  1  1  6  2  1  1  1  2  1  1  1  6  1  2  4  1  1  1  0  1  1  0  1  1  0  2  1  8  0
 0  1  1  0  3  1  1  1  4  7  1 10 14  1  5  1 14 15  1 12  7 14  1  9 15  0  1  1  7 10  1 11 12  1 13  5 10  1  1 12  0  5  1  3  9 13  1  6 14  1  2  1  0  1 11  9 12 14 14  1  2  4  2  1
 0  0  2  0  0  0  8  2  2  2  6  2  4  2 14  2  2 14  4 10  8  0  4  8  6  4  4 14  4 14  0 12  8 10  0  6  4 12  6 10  6 14  4  8  4  4 10  4  0 10 10 14 10  8  6  4  0 14 10  8 10  4  4  0
 0  0  0  2  0  2 10  6 14  2  8  4  8 10 14 12 14  0  2 12  2 10  0  4  6 12 12 10  8  4 10  6  6  0 12  8 12  0  2 10 12 12  6  6  4 10 12  6  2 14  6  2 12  6 14  2  2 12  0 14 12 14  6  0
 0  0  0  0  8  0  8  8  8  0  8  0  8  0  8  0  0  8  8  8  0  8  8  0  8  0  0  0  8  0  0  8  8  0  0  8  0  8  0  8  8  0  0  8  8  0  8  0  0  8  8  8  0  8  8  8  8  0  0  0  8  0  0  8
 0  0  0  0  0  8  8  8  8  8  0  0  0  8  8  0  8  0  8  0  8  8  0  0  8  0  8  0  8  8  0  0  0  8  8  8  8  8  0  0  8  8  0  8  0  0  8  0  8  0  8  0  0  0  0  8  8  0  8  0  0  8  8  8

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

Homogenous weight enumerator: w(x)=1x^0+286x^56+280x^57+1426x^58+1644x^59+3873x^60+4960x^61+7462x^62+8464x^63+8849x^64+8616x^65+7668x^66+4832x^67+3526x^68+1584x^69+1180x^70+288x^71+394x^72+48x^73+110x^74+4x^75+25x^76+6x^78+6x^80+4x^82

The gray image is a code over GF(2) with n=512, k=16 and d=224.
This code was found by Heurico 1.16 in 52.9 seconds.