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  1  1
 0  X  0  X a*X a*X a^2*X a^5*X  0  X a*X 2*X a^2*X 2*X a^2*X a^3*X a^5*X 2*X  0 a*X a^3*X a^3*X a^2*X a^5*X  X a^3*X 2*X  0 a^5*X a*X a^2*X  X a^5*X 2*X a^6*X a^6*X a^6*X a^6*X  0 a^3*X a^3*X 2*X a^6*X a^6*X a^7*X  0  X a*X  X a^6*X a^2*X a^2*X 2*X  0 a^3*X 2*X a^2*X a^6*X a^5*X a*X  X a*X a^3*X a^5*X a^5*X a^6*X  0  X
 0  0  X a^7*X a*X a^2*X a^6*X a^7*X a^3*X a^6*X 2*X a*X 2*X a^2*X  0  0 a^6*X 2*X a^2*X a^6*X a^7*X a^5*X a^5*X a^3*X a^5*X 2*X  0 a^5*X a*X a^7*X a^2*X a^3*X 2*X a^6*X a^7*X a^5*X a*X a^3*X a*X a^2*X a^3*X a^3*X a^6*X a^2*X a*X 2*X a^2*X a^5*X a*X 2*X a^7*X a^3*X a^7*X a^6*X  X  X  X  X  X  0 2*X  X a*X a^2*X a^5*X  0 a^7*X a^5*X

generates a code of length 68 over F9[X]/(X^2) who´s minimum homogenous weight is 531.

Homogenous weight enumerator: w(x)=1x^0+88x^531+312x^540+5832x^544+304x^549+8x^594+8x^603+8x^612

The gray image is a linear code over GF(9) with n=612, k=4 and d=531.
This code was found by Heurico 1.16 in 0.0578 seconds.