The generator matrix

 1  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1 a^2*X a^2*X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 a^3*X  1  1  1  1  1  1
 0  1  1  a a^7*X+a^2 a^3 a^7*X+2 a^7*X+a^6 a^5 a^7  0 a^7 a^5  a a^7*X+a^6 a^7*X+1 a^7*X+a^2 a^3 a^7*X+2  1  0 a^7*X+a^6 a^7 a^5 a^3  a a^7*X+2 a^7*X+a^2 X+a^7  X a^7*X+1 a^6*X+2  1 a^6*X+a^2 a*X a^7*X+1 X+a a^6*X+2 a^6*X+a^6 a^2*X+a 2*X+2 a^6*X+a^2 X+a^5 a^6*X+a^6 a^3*X+a^5 X+a^3 X+a^2  1 a^2*X+a^3 a*X+a  1  1 a^5*X+a^3 a*X+a^7 a^5*X+1 a^5*X+a^6 a^3*X+2 a^3*X+a^6 a*X+a^2 a^3*X+a^5 a^7*X+a^2 a^2*X+a^5 2*X+1 a^6*X+2 a^2*X X+a^5 a^3*X+a^7 a*X+a^7 X+a^5 a^6*X+a^6 a^6*X+1 X+a^3  1 X+a^3 a*X+a^7 a^3*X+a^5  a  0  0
 0  0 a^7*X  0 a^7*X  X a^6*X a^6*X 2*X a*X a^7*X a*X  X  0 a^5*X a^3*X a^6*X 2*X a^3*X  0 a^5*X a^3*X a^5*X a^3*X 2*X a*X a^2*X a^5*X a^7*X  X a*X  0 a^2*X a^6*X a*X  0 a^5*X  X a^3*X 2*X a^2*X a^7*X 2*X a^5*X  X a^3*X  X a*X a^3*X  0 a*X a^5*X  X a^7*X a^7*X 2*X a^7*X 2*X a^2*X a*X  X a^2*X a^2*X a^6*X  0 2*X a^5*X a^2*X a^6*X  0 a^2*X a^5*X a^3*X a^5*X a^3*X a^7*X 2*X a^6*X  0
 0  0  0  X a^7*X a^7*X  X a*X  X a^2*X a^5*X a^6*X a^5*X a*X a^2*X a^7*X  0 a^3*X a*X a^3*X a^6*X a^6*X 2*X a^3*X a*X  X  X a^5*X a*X  0  0 a^6*X a^6*X 2*X a*X a^5*X a^7*X a^3*X 2*X a^6*X a^6*X  0  0 a^7*X a^7*X  X a^6*X a^7*X  0  0 2*X  X 2*X a^5*X a^3*X a^3*X a*X 2*X a^5*X a*X a^3*X  0 a^3*X a^5*X a^6*X a^2*X a^5*X a*X a^3*X a^3*X  0 a*X a^3*X a^2*X a^2*X a^7*X a^7*X a^2*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+72x^595+1112x^603+1584x^604+864x^606+7104x^612+16560x^613+4608x^615+22152x^621+48960x^622+10152x^624+62000x^630+125640x^631+20736x^633+69632x^639+122112x^640+16128x^642+528x^648+496x^657+360x^666+232x^675+160x^684+64x^693+64x^702

The gray image is a linear code over GF(9) with n=711, k=6 and d=594.
This code was found by Heurico 1.16 in 48.3 seconds.