The generator matrix

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

generates a code of length 73 over F8[X]/(X^2) who´s minimum homogenous weight is 503.

Homogenous weight enumerator: w(x)=1x^0+12544x^503+2016x^504+3584x^511+511x^512+12544x^519+1568x^520

The gray image is a linear code over GF(8) with n=584, k=5 and d=503.
This code was found by Heurico 1.16 in 17.7 seconds.