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  2  0  0 12  1  2  2  2  4  2  4  1  1  1  8  2  2  1  8  2  2 12  1  1  0  2  1  1  1  4  1  1  1  2  1
 0  2  0  0  0  2  6 14  0  8  0  2  6 12 14  2  8 14 14  4 12  6 10 12  2  0  2  2  4 10  2  2  2  6  6  8 10  0  2  2  4  2  4  2 10  6  2  4 10  8  0 10 10  4 10  4  4  0  8  0 12 14 12 14
 0  0  2  0  2  2  2  0  4 14  8  0  8 14 10 10  2  6  4  0  4  8 12  6 10  4 12  6  2  4  2 12 14  4 14  2  2  4  4  8 14  2  4  2  6  8  2  8 10  6  2 10 14  2  0 14  0  6  2  2  6 14  8  0
 0  0  0  2  2  0  2 10  8  2 14 14  4 12 14 12  6  4  2  6  0  8  8  8 10  6 14  0 14  2  2  4  8 10  8  0 10  2 14  2 12 12  6  4  6 10  2  2 12 14  6  0  4  6  0  8  8 12  4 12 10  2 14  4
 0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  8  8  8  0  0  8  0  8  0  0  8  0  8  0  8  8  8  8  8  0  8  8  8  0  8  0  0  0  8  8  0  0  8  0  8  0  0  0  0
 0  0  0  0  0  8  0  8  8  8  8  0  8  8  8  0  8  8  8  8  8  8  0  0  8  0  0  0  0  0  8  8  8  0  8  0  0  8  8  8  8  0  8  0  0  0  0  0  8  8  8  0  8  0  0  0  8  0  8  0  8  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+190x^56+496x^57+807x^58+1440x^59+1531x^60+2854x^61+2846x^62+4116x^63+4050x^64+4392x^65+3028x^66+2902x^67+1489x^68+1128x^69+621x^70+410x^71+213x^72+144x^73+49x^74+26x^75+12x^76+10x^77+8x^78+2x^79+2x^80+1x^86

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 18.1 seconds.