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  X  1  X  X  X  X  X  X  X  1  X  X  X  1  X  1  1  X  X  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1
 0 2X  0  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0 2X  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0 2X  0 2X 2X  0  0  0 2X 2X 2X 2X  0  0  0  0  0 2X 2X  0 2X 2X  0  0 2X 2X  0 2X
 0  0 2X  0  0  0 2X 2X 2X 2X 2X  0 2X 2X  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0 2X  0  0 2X 2X 2X  0  0  0 2X 2X 2X 2X  0  0  0  0  0  0 2X 2X  0 2X 2X  0 2X 2X 2X 2X  0  0
 0  0  0 2X  0 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X  0 2X  0 2X 2X  0  0 2X 2X  0  0  0 2X 2X 2X  0 2X 2X 2X  0  0  0  0 2X  0 2X
 0  0  0  0 2X 2X  0 2X 2X  0 2X 2X 2X  0  0 2X  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0  0 2X 2X  0 2X 2X 2X 2X  0  0  0 2X 2X  0  0  0  0 2X 2X  0 2X  0 2X  0  0 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+15x^62+222x^63+15x^64+2x^79+1x^94

The gray image is a code over GF(2) with n=504, k=8 and d=248.
This code was found by Heurico 1.16 in 0.125 seconds.