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

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

Homogenous weight enumerator: w(x)=1x^0+110x^56+164x^57+507x^58+444x^59+910x^60+1476x^61+1319x^62+2636x^63+1613x^64+2460x^65+1315x^66+1364x^67+769x^68+460x^69+375x^70+164x^71+157x^72+48x^73+58x^74+19x^76+6x^78+3x^80+4x^82+2x^84

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 5.18 seconds.