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

generates a code of length 75 over F9[X]/(X^2) who´s minimum homogenous weight is 567.

Homogenous weight enumerator: w(x)=1x^0+368x^567+1176x^576+1224x^585+5832x^592+744x^594+46656x^601+840x^603+704x^612+432x^621+368x^630+312x^639+240x^648+112x^657+40x^666

The gray image is a linear code over GF(9) with n=675, k=5 and d=567.
This code was found by Heurico 1.16 in 1.6 seconds.