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

generates a code of length 73 over F9[X]/(X^2) who´s minimum homogenous weight is 549.

Homogenous weight enumerator: w(x)=1x^0+176x^549+1016x^558+1240x^567+1064x^576+52488x^584+736x^585+640x^594+496x^603+400x^612+384x^621+240x^630+128x^639+24x^648+16x^657

The gray image is a linear code over GF(9) with n=657, k=5 and d=549.
This code was found by Heurico 1.16 in 1.55 seconds.