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

generates a code of length 79 over F9[X]/(X^2) who´s minimum homogenous weight is 594.

Homogenous weight enumerator: w(x)=1x^0+120x^594+880x^603+1176x^612+648x^616+960x^621+10368x^625+752x^630+41472x^634+736x^639+576x^648+384x^657+384x^666+304x^675+168x^684+104x^693+16x^702

The gray image is a linear code over GF(9) with n=711, k=5 and d=594.
This code was found by Heurico 1.16 in 1.71 seconds.