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

generates a code of length 63 over F8[X]/(X^2) who´s minimum homogenous weight is 416.

Homogenous weight enumerator: w(x)=1x^0+539x^416+56x^420+693x^424+1176x^428+777x^432+8232x^436+553x^440+19208x^444+469x^448+287x^456+301x^464+175x^472+133x^480+140x^488+28x^496

The gray image is a linear code over GF(8) with n=504, k=5 and d=416.
This code was found by Heurico 1.16 in 0.693 seconds.