The generator matrix

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

generates a code of length 74 over F8[X]/(X^2) who´s minimum homogenous weight is 510.

Homogenous weight enumerator: w(x)=1x^0+12544x^510+2527x^512+3584x^518+12544x^526+1568x^528

The gray image is a linear code over GF(8) with n=592, k=5 and d=510.
This code was found by Heurico 1.16 in 69.4 seconds.