The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+44x^56+66x^57+277x^58+410x^59+1055x^60+1088x^61+1868x^62+2056x^63+2761x^64+2036x^65+1932x^66+1052x^67+942x^68+374x^69+245x^70+48x^71+48x^72+16x^73+18x^74+10x^75+11x^76+2x^77+6x^78+8x^79+2x^80+2x^81+4x^82+1x^86+1x^90

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 3.65 seconds.