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

generates a code of length 64 over Z16 who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+78x^55+281x^56+446x^57+857x^58+1028x^59+1796x^60+2330x^61+3616x^62+3592x^63+4513x^64+4236x^65+3390x^66+2238x^67+1874x^68+926x^69+693x^70+316x^71+269x^72+106x^73+80x^74+32x^75+30x^76+20x^77+3x^78+10x^79+4x^80+1x^82+2x^83

The gray image is a code over GF(2) with n=512, k=15 and d=220.
This code was found by Heurico 1.16 in 19.7 seconds.