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

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

Homogenous weight enumerator: w(x)=1x^0+275x^54+412x^55+1109x^56+1452x^57+2873x^58+3024x^59+5104x^60+5820x^61+9099x^62+7228x^63+8956x^64+5828x^65+5548x^66+3220x^67+2498x^68+1268x^69+997x^70+312x^71+285x^72+96x^73+75x^74+12x^75+30x^76+12x^78+1x^80+1x^94

The gray image is a code over GF(2) with n=504, k=16 and d=216.
This code was found by Heurico 1.16 in 67.7 seconds.