The generator matrix

 1  0  0  0  1  1  1  1 2X+2  1  1  1 X+2  X  X  1  1  1  1  1 2X+2 2X  1 2X+2 3X+2  1  1  2  2 3X 2X  1  1 2X  1  1  1 2X  1  1  1 X+2  1 3X 2X X+2 2X+2  1 3X 2X+2 3X+2  1  1  1  1  1 3X  1  1  1  X 2X  X
 0  1  0  0  X 2X+3 2X+1  2  1 X+3 3X+2 X+1  1 2X+2  1  X 3X+2  0 2X+1 X+1  1 3X  3  0  1 2X  1  1 2X  1  1  X 3X+2  1 3X+3  2 2X  2 X+2 2X+3  2  1 X+1  1  1  0  1 X+1  1  1  X 2X+2 X+1 2X+2 3X+1 2X+1  1  2 X+2  2  1  1 X+2
 0  0  1  0  0 2X+2  1 2X+3 2X+3 2X 2X+1 X+1 2X+1  1  X 3X+1 2X+1 3X 3X+1 2X+3 3X+3  1 3X  1 X+2 3X 3X+2 X+3  X 3X+2 2X+1 3X+3  X 3X+2 2X+1  X 3X+2  1 3X+1 2X+2 2X+3 3X+3 2X+1  2 2X+2  1 X+3 X+1 3X+1 2X  1 2X+2 2X+2  2  0  1  0 3X+3  0 3X+3  0 X+3 2X+2
 0  0  0  1  1 3X+3 2X+2 X+1 3X+3 3X  X 3X+3  X 3X+3  1  1  0 X+3 3X+3  0  3 2X+1 2X+1  X 3X+2 2X  2 3X  1 X+1 2X+3  0  X 3X X+1 2X+1  X 3X+1 3X+1 X+3 2X+2  0 2X  X 2X+1  X X+3 3X  3 2X+1 3X+1 3X+2 2X+2 3X 3X+2 3X X+1 3X+1  0  3 2X 2X+2  1
 0  0  0  0 2X+2  0  0  0  0 2X+2 2X+2 2X+2  2 2X+2  2 2X  2  2  2 2X  0  2 2X 2X  0  0 2X+2 2X+2  2 2X 2X+2  0  2  2 2X 2X+2  2 2X  2 2X+2  2 2X+2 2X+2 2X 2X+2  0 2X  0 2X+2  0 2X  2 2X+2 2X 2X  0 2X+2  0 2X 2X+2  0  0 2X

generates a code of length 63 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+428x^55+1892x^56+4214x^57+8288x^58+13006x^59+21538x^60+27506x^61+35352x^62+36714x^63+35985x^64+28600x^65+21965x^66+12706x^67+7635x^68+3544x^69+1708x^70+662x^71+271x^72+84x^73+13x^74+16x^75+5x^76+2x^77+2x^78+4x^79+2x^81+1x^88

The gray image is a code over GF(2) with n=504, k=18 and d=220.
This code was found by Heurico 1.16 in 574 seconds.