The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+63x^54+40x^55+328x^56+228x^57+706x^58+724x^59+1341x^60+1572x^61+2192x^62+2052x^63+2253x^64+1548x^65+1354x^66+732x^67+577x^68+236x^69+241x^70+36x^71+78x^72+32x^74+25x^76+16x^78+4x^80+4x^82+1x^84

The gray image is a code over GF(2) with n=504, k=14 and d=216.
This code was found by Heurico 1.16 in 5.96 seconds.