The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+174x^56+156x^57+580x^58+796x^59+1753x^60+2560x^61+3664x^62+4116x^63+5279x^64+4240x^65+3590x^66+2596x^67+1606x^68+720x^69+460x^70+172x^71+166x^72+4x^73+68x^74+37x^76+20x^78+4x^80+2x^82+4x^84

The gray image is a code over GF(2) with n=512, k=15 and d=224.
This code was found by Heurico 1.16 in 23.9 seconds.