The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+13x^54+54x^55+89x^56+116x^57+243x^58+448x^59+441x^60+1100x^61+776x^62+1684x^63+767x^64+1100x^65+413x^66+448x^67+217x^68+116x^69+76x^70+54x^71+9x^72+7x^74+5x^76+6x^78+5x^80+1x^82+1x^84+1x^86+1x^96

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 1.49 seconds.