The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1 a^7*X  1  1 a^6*X  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 a*X  1  1  1  1  1  1  1 a^2*X  1  1 a^2*X 2*X  1  1
 0  1  0 a^7*X a*X a^6*X a^5*X 2*X  1 a^7*X+2 a^7*X+1  2  1 a^6*X+1 a^6*X+2  1  a a^2 a^7*X+a a^7*X+a^3 a^3 a^7*X+a^6 a^6 a^7*X+a^5 a*X+a a^5*X+a^6 a^6*X+a^5 a^2*X+a^7 a^2*X+a 2*X+a^2 a*X+a^7 X+a^3 a^2*X+2 a^7*X+a^2 a*X+a^5 a^6*X+a^2 a^5*X+1 a^5*X+2 a^3*X+a^7 a^2*X+a^3 a^5*X+a^7 a^5 a^7*X+1 a^3*X+a^7 a*X+a^6 X+a^5 X+a^7 a^5*X+a^2 a^6*X+a^3 a^3*X+a^3 a^3*X+a^6 a^6*X+a^5 X+a a^7*X+a a^2*X+a^2 a*X+a^3 a^6*X+a^7  1 a^3*X+a^6 a^3*X+a^5 a^6*X+a  1  1 a^7*X+a^6 a^6*X+2 a^7*X+2  1 a^2*X+a^2  X a^5*X+a^3  1 2*X+a^6 a^5*X+a^3  1  1 a^3*X+1 X+2
 0  0  1 a^7*X+1  a a^2 a^7*X+2 a^7*X+a^7 a^6 a^7*X+a^5 a^7*X+a^3 X+a^6 a^7*X+2 a^5 a^3  1 a*X a^2*X+a^6 a^7*X+a^2 2*X+1 2*X+a a^6*X+a X+1 2*X+a^6 X+a^3 a^6*X+a^5 a^5*X+2  2 X+a 2*X X+a^5 a^6*X+a^3 a^5*X+a^7 a^5*X+a^3 a^5*X+a^2 a^3*X+1 2*X+a^7 a^2*X+1 a^5*X+a a^6 a^2*X+a^2 X+a^5 a^6*X a*X+a^3 a*X+2 a*X+a^7 a^3*X+a^7 a^2*X+a^7 a^6*X X+a^2 a^2*X+a^3  0 a^6*X+2 2*X+1 a^3*X+a^2 a^7*X+a^5 a*X a^3*X+a^6 a^5*X+a^2  1 a^5*X+a^5 a*X+a^2 a^2*X+a^5 a^2*X+a^6 a^7*X X+a^2 a^3*X+2 a^2*X+a^5 a^6*X+a^6 a^5*X+2 a^2*X+a a^5*X+a^7 X+a^7 X+a^3 a^3*X+a^7 a^7*X+a^2 X+2

generates a code of length 77 over F9[X]/(X^2) who´s minimum homogenous weight is 597.

Homogenous weight enumerator: w(x)=1x^0+9216x^597+15264x^598+6912x^599+432x^602+1528x^603+3240x^604+48960x^606+47520x^607+14904x^608+1728x^611+3888x^612+5184x^613+71424x^615+69120x^616+20736x^617+3672x^620+6928x^621+9072x^622+92016x^624+78048x^625+21600x^626+24x^639+16x^648+8x^657

The gray image is a linear code over GF(9) with n=693, k=6 and d=597.
This code was found by Heurico 1.16 in 39 seconds.