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

generates a code of length 64 over Z16 who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+248x^55+486x^56+1106x^57+1476x^58+2530x^59+3066x^60+5470x^61+6002x^62+8622x^63+7536x^64+8508x^65+6282x^66+5594x^67+3074x^68+2502x^69+1208x^70+890x^71+400x^72+272x^73+126x^74+60x^75+24x^76+28x^77+10x^78+8x^79+5x^80+2x^81

The gray image is a code over GF(2) with n=512, k=16 and d=220.
This code was found by Heurico 1.16 in 91.2 seconds.