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

generates a code of length 63 over Z16 who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+38x^55+214x^56+346x^57+655x^58+730x^59+1244x^60+1734x^61+2009x^62+2580x^63+2118x^64+1722x^65+1158x^66+634x^67+446x^68+280x^69+248x^70+108x^71+66x^72+10x^73+19x^74+4x^75+6x^76+2x^77+6x^78+2x^79+1x^80+2x^81+1x^94

The gray image is a code over GF(2) with n=504, k=14 and d=220.
This code was found by Heurico 1.16 in 5.1 seconds.