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

generates a code of length 77 over F9[X]/(X^2) who´s minimum homogenous weight is 599.

Homogenous weight enumerator: w(x)=1x^0+576x^599+112x^603+1080x^604+6048x^605+6048x^606+2592x^607+2088x^608+288x^612+1728x^613+6048x^614+3456x^615+648x^616+576x^617+216x^621+3024x^622+11232x^623+7992x^624+2592x^625+2592x^626+80x^630+16x^639+8x^648+8x^666

The gray image is a linear code over GF(9) with n=693, k=5 and d=599.
This code was found by Heurico 1.16 in 0.626 seconds.