The generator matrix

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

generates a code of length 64 over Z16 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+40x^54+112x^55+231x^56+666x^57+923x^58+2184x^59+2933x^60+5566x^61+6485x^62+9332x^63+8468x^64+9510x^65+6553x^66+5626x^67+2994x^68+2078x^69+750x^70+610x^71+191x^72+88x^73+83x^74+54x^75+23x^76+12x^77+12x^78+2x^79+5x^80+1x^82+2x^84+1x^94

The gray image is a code over GF(2) with n=512, k=16 and d=216.
This code was found by Heurico 1.16 in 47.7 seconds.