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

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

Homogenous weight enumerator: w(x)=1x^0+84x^54+290x^55+582x^56+858x^57+1384x^58+2220x^59+3566x^60+4246x^61+7700x^62+6618x^63+10256x^64+6992x^65+7646x^66+4258x^67+3732x^68+2008x^69+1307x^70+830x^71+402x^72+262x^73+129x^74+48x^75+50x^76+34x^77+21x^78+6x^79+3x^80+1x^82+2x^83

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 75.3 seconds.