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

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

Homogenous weight enumerator: w(x)=1x^0+130x^54+52x^55+444x^56+248x^57+898x^58+792x^59+1813x^60+2088x^61+3619x^62+4048x^63+4709x^64+3960x^65+3627x^66+2008x^67+1840x^68+824x^69+752x^70+252x^71+331x^72+48x^73+166x^74+16x^75+67x^76+17x^78+10x^80+5x^82+2x^86+1x^88

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 22.1 seconds.