The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 a^6*X  1  X  1  1  1  1  1 a*X  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1 a^2*X  1  1  1  1  1  1  1  1  1  1
 0  1  0 a^6*X a*X a^4*X  X a^5*X a^3*X a^2*X  1 a^6*X+a a^2 a^6*X+1 a^5*X+a a^6*X+a^2 a^6*X+a^5 X+1 a^4*X+a X+a^5 X+a^2  1 a^5  1  a a^2*X+1 a^6*X+a^6 a^4*X+a^6 a^6  1 a*X+a^6 a^2 a^4*X+a^5 a^5*X+a^3 a^6*X+a^3 a^3*X+a^3 a*X+a^3 a^5*X+a^6 a^3*X+a^5  1 a^4*X+a^2 a^2*X+1 X+a a^6*X+a^2 a^6*X+a^4 a^5*X+1 X+a^5 X+a^3 a^4*X+a^4 a^3*X+a^4 a^5*X+a^4 a^4  1 a^5*X+a a^5*X+a^3 a^4*X+a^5 a^4 X+a^6 a^3*X+a^3 a*X+a^2 X+a a*X+a^5 a*X
 0  0  1  1  a a^2 a^6*X+a^3 a^6*X+a^4 a^5 a^6 X+a^6 a^2*X+a^6 a*X+a^6 a*X+a^5 a^6*X+1 a^3 X+a^2 a^6*X+a^2 a^4 a^3*X+a a^3*X+a^4  1 X+a^5 a^5*X+a^3 a^5*X+a^3 a^4*X+a a^3*X+a^5 a*X+1 X+a^3 a^3*X+a^5 a*X a^5*X+a^2 a^4*X a^3*X+1 a^4*X+a^4 a^4*X+a a^6*X+a^5 a^3*X+a^2 a*X+a^3 a^6*X+a^6  a a^6*X+a^4 a^2*X a^5 a^3*X+a^4  X a^6*X+a^6 a^3*X+a^3 a^3 a^5*X+1 X+a^6 a^6*X a*X+a^4 a*X+a a^3*X+a^2 a^3*X+1 a^3*X+a^5 X+a^4 a^6 a^4*X+1 a^6*X+a^2 a^3*X+a a^6*X

generates a code of length 63 over F8[X]/(X^2) who´s minimum homogenous weight is 424.

Homogenous weight enumerator: w(x)=1x^0+2702x^424+7616x^425+4368x^426+728x^427+168x^428+19075x^432+28952x^433+13104x^434+3640x^435+1008x^436+26327x^440+37520x^441+13104x^442+3976x^443+2408x^444+34825x^448+44184x^449+16016x^450+2408x^451+7x^480+7x^488

The gray image is a linear code over GF(8) with n=504, k=6 and d=424.
This code was found by Heurico 1.16 in 12.3 seconds.