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  1  1  1  1  1  1  2  2  2  1  1  1  1  2  2  1  1  2  4  2  2  1  1  4  1  2  1  4  1  2  1  2  1  8  4  1  1  1
 0 12  0  0  0  4 12  4  0  8  4 12  0  8 12  0  4  4  8  4 12 12  8  8 12  0 12 12  4  8  4 12  0  8 12  8  8  0  8 12 12 12  4  0 12 12  0  8 12  0 12 12  8  8  8  4 12 12  8  4 12  4 12 12
 0  0 12  0  4  4 12  0  0  0  4  8  4  4  0  8  4  4 12  8 12  0  8  8  4 12  0  0 12  8  4 12  4 12  4 12  0  4  0  8  0 12  4  8  4 12  8  0  4  8  0  0 12 12  8  4  0  4  4  4  4  4  0  0
 0  0  0 12  4  0 12  4  0  4 12  8 12  0  4  8  8  8  4  0  4  4 12  4  4 12  4  8  0  8  8  0 12 12 12  8  0  0  0  0  0  0  0  4  4  4 12  4  0  4  4 12  0  4  8  4  8  0 12  8 12  0 12  0
 0  0  0  0  8  0  0  0  8  0  8  8  0  0  0  0  8  8  8  0  8  8  0  0  0  0  8  8  0  8  0  8  8  8  0  0  8  0  8  8  0  0  8  0  0  0  0  8  0  0  8  8  8  0  0  0  0  8  0  8  8  0  8  8
 0  0  0  0  0  8  0  0  8  8  8  0  8  0  8  8  0  8  8  0  8  8  0  8  0  0  0  0  8  0  0  0  0  8  8  8  8  8  8  0  8  0  8  8  0  8  0  8  8  8  8  0  8  0  0  8  8  8  8  8  0  0  8  8
 0  0  0  0  0  0  8  0  0  0  0  0  0  8  8  8  0  0  8  8  8  8  0  0  0  8  0  8  8  8  0  8  8  0  8  0  8  8  0  8  8  0  8  8  0  0  0  8  0  0  0  0  8  0  8  8  0  8  8  0  0  0  0  8
 0  0  0  0  0  0  0  8  8  8  0  8  0  0  0  0  0  8  0  8  8  0  8  0  8  0  8  0  0  8  8  0  0  8  0  0  0  0  0  8  8  0  8  8  0  8  8  8  8  8  8  8  0  0  8  0  0  8  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+118x^54+313x^56+48x^57+458x^58+320x^59+521x^60+952x^61+1589x^62+2736x^63+2366x^64+2824x^65+1520x^66+992x^67+433x^68+264x^69+386x^70+48x^71+255x^72+8x^73+132x^74+69x^76+19x^78+8x^80+2x^82+1x^84+1x^96

The gray image is a code over GF(2) with n=512, k=14 and d=216.
This code was found by Heurico 1.16 in 7.59 seconds.