The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+82x^57+157x^58+310x^59+466x^60+646x^61+869x^62+1034x^63+1205x^64+1040x^65+824x^66+612x^67+406x^68+272x^69+105x^70+60x^71+18x^72+16x^73+19x^74+14x^75+13x^76+6x^77+7x^78+2x^79+2x^80+2x^81+2x^82+1x^84+1x^94

The gray image is a code over GF(2) with n=512, k=13 and d=228.
This code was found by Heurico 1.16 in 2.23 seconds.