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

generates a code of length 64 over Z16 who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+305x^58+136x^59+616x^60+480x^61+1118x^62+928x^63+1318x^64+984x^65+870x^66+376x^67+504x^68+128x^69+220x^70+32x^71+112x^72+8x^73+41x^74+8x^76+6x^78+1x^96

The gray image is a code over GF(2) with n=512, k=13 and d=232.
This code was found by Heurico 1.16 in 28.6 seconds.