The generator matrix

 1  0  1  1  1  4  1  1 14  1 10  1  8  1  1  1  6  1  1  6  1  1  1  1  0  1  1  1  1  1  2  1  2  1 12  1  1 10  1  4  1 12  1  1  0  4  1 10  0  1  1  1  1  1  1  1  6 12  8  4  1  1  8
 0  1  1  4  3  1  2  7  1 13  1  6  1  5 12 11  1 12  6  1  7 14 13  8  1 15  0  0 14 12  1 11  1  1  1  2  9  1 10  2 11  1 14  7  1  4 14  1  8  9  0  1 11  6  0  0  1  1  2  2 12 12  2
 0  0  2  2  0  2  2  2  4  4  6  0  4  8  6 10  0  0 14  6 12  4  2  4 14 14  0  6 10 10 10  4 10 12  0  4 14  8 14  2 12  6  0 10  8  2  2  4  2 14  8  4 12  4 12 12 14 10 10 14  8  6  4
 0  0  0  8  0  0  0  0  0  8  8  0  0  0  0  8  8  8  8  0  8  0  8  8  0  0  0  8  0  8  8  8  0  8  0  0  0  8  0  8  0  8  0  8  8  8  0  0  8  0  0  0  8  8  0  0  8  8  0  8  8  0  8
 0  0  0  0  8  0  0  0  0  8  0  0  0  8  0  0  0  0  0  0  8  8  0  8  8  8  0  8  8  8  0  0  0  8  0  8  8  8  0  8  0  0  8  0  8  8  0  8  0  8  0  8  0  0  8  8  0  0  8  0  8  8  0
 0  0  0  0  0  8  0  0  0  0  8  8  8  8  0  0  8  0  0  8  8  0  8  8  8  0  0  8  8  8  0  8  0  8  8  8  8  0  0  0  0  8  0  0  0  0  8  8  8  0  0  0  8  8  0  8  0  0  8  8  0  0  0
 0  0  0  0  0  0  8  0  0  8  8  0  0  0  8  8  8  8  0  0  8  0  8  8  0  0  0  0  8  0  0  8  8  0  8  8  8  0  0  8  8  0  0  8  8  0  0  0  0  8  8  8  8  0  8  8  0  8  0  8  0  0  0
 0  0  0  0  0  0  0  8  8  0  0  0  8  0  8  8  0  8  8  8  8  0  0  0  0  8  8  0  0  8  0  8  8  8  8  0  8  0  8  0  8  8  8  0  0  8  8  8  0  0  0  0  0  0  0  8  8  0  8  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+148x^54+156x^55+732x^56+780x^57+2301x^58+2856x^59+5693x^60+6284x^61+9585x^62+8476x^63+9633x^64+6452x^65+5760x^66+2724x^67+2149x^68+772x^69+552x^70+120x^71+198x^72+48x^73+71x^74+4x^75+21x^76+11x^78+4x^80+4x^82+1x^84

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 47.9 seconds.