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

generates a code of length 87 over F9[X]/(X^2) who´s minimum homogenous weight is 684.

Homogenous weight enumerator: w(x)=1x^0+120x^684+240x^693+5832x^696+360x^702+8x^783

The gray image is a linear code over GF(9) with n=783, k=4 and d=684.
This code was found by Heurico 1.16 in 0.122 seconds.