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

generates a code of length 77 over F9[X]/(X^2) who´s minimum homogenous weight is 585.

Homogenous weight enumerator: w(x)=1x^0+688x^585+1144x^594+1032x^603+5832x^608+952x^612+46656x^617+696x^621+576x^630+520x^639+296x^648+328x^657+224x^666+56x^675+32x^684+16x^693

The gray image is a linear code over GF(9) with n=693, k=5 and d=585.
This code was found by Heurico 1.16 in 1.62 seconds.