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

generates a code of length 73 over F8[X]/(X^2) who´s minimum homogenous weight is 464.

Homogenous weight enumerator: w(x)=1x^0+413x^464+1554x^472+2450x^480+3066x^488+3339x^496+32669x^504+204596x^512+4081x^520+3710x^528+2786x^536+2002x^544+931x^552+476x^560+49x^568+21x^576

The gray image is a linear code over GF(8) with n=584, k=6 and d=464.
This code was found by Heurico 1.16 in 48.1 seconds.