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

generates a code of length 76 over F9[X]/(X^2) who´s minimum homogenous weight is 589.

Homogenous weight enumerator: w(x)=1x^0+12024x^589+16272x^590+2016x^591+216x^593+24x^594+60696x^598+49680x^599+4320x^600+1512x^602+304x^603+91368x^607+73440x^608+11232x^609+4104x^611+384x^612+115848x^616+82224x^617+5760x^618+8x^657+8x^675

The gray image is a linear code over GF(9) with n=684, k=6 and d=589.
This code was found by Heurico 1.16 in 49.5 seconds.