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

generates a code of length 63 over Z16 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+42x^54+68x^55+99x^56+164x^57+247x^58+328x^59+623x^60+828x^61+1083x^62+1370x^63+1056x^64+852x^65+583x^66+274x^67+179x^68+100x^69+92x^70+50x^71+44x^72+40x^73+29x^74+14x^75+14x^76+3x^78+8x^79+1x^98

The gray image is a code over GF(2) with n=504, k=13 and d=216.
This code was found by Heurico 1.16 in 1.78 seconds.