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

generates a code of length 64 over Z16 who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+200x^57+355x^58+730x^59+889x^60+1432x^61+1573x^62+2078x^63+2162x^64+2182x^65+1507x^66+1156x^67+803x^68+522x^69+265x^70+272x^71+109x^72+106x^73+7x^74+18x^75+4x^76+6x^77+2x^78+2x^79+2x^82+1x^90

The gray image is a code over GF(2) with n=512, k=14 and d=228.
This code was found by Heurico 1.16 in 4.89 seconds.