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

generates a code of length 69 over F9[X]/(X^2) who´s minimum homogenous weight is 522.

Homogenous weight enumerator: w(x)=1x^0+704x^522+1064x^531+1224x^540+5832x^544+904x^549+46656x^553+720x^558+512x^567+560x^576+448x^585+136x^594+208x^603+72x^612+8x^621

The gray image is a linear code over GF(9) with n=621, k=5 and d=522.
This code was found by Heurico 1.16 in 1.69 seconds.