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

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

Homogenous weight enumerator: w(x)=1x^0+121x^58+410x^59+484x^60+684x^61+940x^62+984x^63+1199x^64+1144x^65+751x^66+480x^67+382x^68+226x^69+126x^70+96x^71+69x^72+56x^73+14x^74+14x^75+8x^76+2x^85+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 1.29 seconds.