The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+80x^55+224x^56+644x^57+1040x^58+2088x^59+3345x^60+4892x^61+7196x^62+8064x^63+10008x^64+8370x^65+7668x^66+5034x^67+3108x^68+1826x^69+916x^70+554x^71+189x^72+130x^73+64x^74+38x^75+19x^76+10x^77+8x^78+14x^79+1x^80+4x^82+1x^88

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 51.4 seconds.