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.