The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+131x^54+24x^55+432x^56+264x^57+1109x^58+1016x^59+4045x^60+3648x^61+9694x^62+6296x^63+12231x^64+6272x^65+9864x^66+3720x^67+3878x^68+1056x^69+1037x^70+208x^71+314x^72+24x^73+155x^74+75x^76+26x^78+14x^80+2x^84

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 52.5 seconds.