The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+180x^56+172x^57+588x^58+924x^59+1776x^60+2132x^61+4104x^62+3884x^63+5334x^64+3996x^65+3952x^66+2196x^67+1811x^68+860x^69+400x^70+164x^71+157x^72+8x^73+58x^74+43x^76+12x^78+8x^80+6x^82+2x^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 14.2 seconds.