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

generates a code of length 64 over Z16 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+89x^56+136x^57+426x^58+612x^59+1014x^60+1236x^61+1740x^62+1928x^63+2402x^64+1896x^65+1562x^66+1100x^67+942x^68+532x^69+286x^70+192x^71+157x^72+40x^73+44x^74+8x^75+23x^76+6x^78+10x^80+1x^84+1x^88

The gray image is a code over GF(2) with n=512, k=14 and d=224.
This code was found by Heurico 1.16 in 5.25 seconds.