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  1  1  1  1  1  1  1  2  2 12  2  2  8  8  1  1  4 12  2  1  0  1  1  8  2  1  0  1  1  1  4  2  4  1  2  1  8  1  1 12  1
 0  2  0  0  0  2 14  2  4 12 14 10 12 14 12 14  4 14  0  4  2  6 12  8 14  8 12  4  0 14  0 14  2  0  6  2  8 14  0  2  2 10  0  4  6  4  8  8  4  8 14 10  6  8 10  2  4  6  0  2  0  2  2  2
 0  0  2  0  2  2 10  8  0  0  2 10  6  4 14  4  8  8  4  2 14  6 14  4 12 14  2 10 12 10  2  2  6 14  4  0  2 14  6 10 14 12  8  2  4  6 12 12 14  2  0 14  4  2  0  0  4  2 14  2  0 14 10  0
 0  0  0  2  2  8  2  6 14  4  4 14 14 10 12  4 10 14 12  6 12 10  4 12  8 14  8  6 14  4 14  0 10  0 12  2  8 14 14  0  0  0 14  6  4  0  2  2  0 14 12  2  0  0 12 14 10  8 10  6  6  6  2  6
 0  0  0  0  4  0  4 12 12 12 12  8  8  0 12 12 12  0  0  4  0  8  8 12  8 12  4  0  0  0  4  0  4 12  8  8  0 12  8 12  8  4  4 12  0  4 12  8 12 12  4  0  4  8  8  4  4  4 12  8 12  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+234x^56+420x^57+824x^58+1160x^59+1864x^60+2392x^61+3454x^62+3972x^63+4335x^64+4044x^65+3374x^66+2416x^67+1751x^68+980x^69+668x^70+376x^71+248x^72+96x^73+126x^74+8x^75+9x^76+4x^77+2x^78+4x^79+5x^80+1x^88

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 18.5 seconds.