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

generates a code of length 63 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+63x^62+896x^63+63x^64+1x^126

The gray image is a code over GF(2) with n=504, k=10 and d=248.
This code was found by Heurico 1.16 in 0.312 seconds.