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

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

Homogenous weight enumerator: w(x)=1x^0+82x^58+170x^59+181x^60+304x^61+405x^62+556x^63+729x^64+586x^65+419x^66+266x^67+140x^68+124x^69+61x^70+32x^71+16x^72+10x^73+6x^74+3x^76+2x^78+2x^80+1x^106

The gray image is a code over GF(2) with n=512, k=12 and d=232.
This code was found by Heurico 1.16 in 0.658 seconds.