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

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

Homogenous weight enumerator: w(x)=1x^0+26x^54+114x^55+257x^56+548x^57+662x^58+1196x^59+1276x^60+2904x^61+2656x^62+5014x^63+3555x^64+4932x^65+2747x^66+2936x^67+1306x^68+1196x^69+485x^70+430x^71+231x^72+136x^73+66x^74+28x^75+22x^76+12x^77+8x^78+10x^79+4x^80+5x^82+4x^84+1x^86

The gray image is a code over GF(2) with n=512, k=15 and d=216.
This code was found by Heurico 1.16 in 19 seconds.