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  1  2  1  1  2  1  1  1  2  1  1  1  1  2  4  1  1  1  1  4  1  0  4  1  2  1  4  2  2  2  1
 0 12  0  0  0  4 12  4  8 12  8 12  0  4  8 12  0 12  0 12  0  8  4 12  8  8 12 12  0  4  0  4  4  8 12  8 12  0 12 12  8 12  8 12  4 12 12  8  8  0  8 12  4  4  0  0  0 12  0 12 12  0 12  0
 0  0 12  0  4  4  4  8  0  4  8  4  4  0 12  8  0 12 12  0  0 12 12  8  0  8  0  8 12 12 12 12  4 12  4  0  0 12 12  0  0 12  8  0  8  4  8  0  4  4  8  8  8 12  0 12  8  0  4 12 12 12  8  8
 0  0  0 12  4  0  4  4  8  0 12  4  4  4  8  8  8  8  4  4  0  4  0 12  4  4  8  8  0  4  8 12  0  0 12  0 12  0  8 12  4  4 12  0  8  0  0  4  4 12  8  0 12 12  4  0  8  8  4  4 12  0  0  4
 0  0  0  0  8  0  0  8  8  8  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  8  8  8  8  0  8  0  0  8  8  0  8  8  0  0  0  0  8  0  8  0  8  8  8  8  8  8  8  8  0  8  8  8  8
 0  0  0  0  0  8  0  0  0  0  8  8  0  8  8  8  8  0  8  0  8  8  8  8  8  0  0  8  8  8  0  0  8  0  8  0  8  8  8  8  0  0  8  8  0  0  0  0  8  8  8  8  0  8  8  0  0  8  8  0  8  0  0  0

generates a code of length 64 over Z16 who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+58x^57+107x^58+108x^59+136x^60+370x^61+201x^62+1044x^63+198x^64+1020x^65+166x^66+320x^67+108x^68+58x^69+48x^70+46x^71+25x^72+22x^73+19x^74+16x^75+11x^76+8x^77+3x^78+2x^79+1x^100

The gray image is a code over GF(2) with n=512, k=12 and d=228.
This code was found by Heurico 1.16 in 16.4 seconds.