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

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

Homogenous weight enumerator: w(x)=1x^0+37x^56+224x^57+369x^58+694x^59+870x^60+1368x^61+1524x^62+2056x^63+2161x^64+2286x^65+1579x^66+1200x^67+687x^68+560x^69+298x^70+220x^71+100x^72+54x^73+36x^74+34x^75+13x^76+4x^77+4x^79+2x^80+2x^82+1x^88

The gray image is a code over GF(2) with n=512, k=14 and d=224.
This code was found by Heurico 1.16 in 5.12 seconds.