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

generates a code of length 64 over Z16 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+52x^54+122x^55+189x^56+246x^57+293x^58+532x^59+687x^60+1120x^61+1675x^62+2040x^63+2507x^64+2200x^65+1595x^66+1172x^67+658x^68+382x^69+285x^70+194x^71+113x^72+112x^73+88x^74+32x^75+34x^76+34x^77+12x^78+4x^79+2x^80+2x^81+1x^92

The gray image is a code over GF(2) with n=512, k=14 and d=216.
This code was found by Heurico 1.16 in 7.42 seconds.