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

generates a code of length 90 over F9[X]/(X^2) who´s minimum homogenous weight is 684.

Homogenous weight enumerator: w(x)=1x^0+272x^684+1160x^693+1048x^702+648x^704+1000x^711+10368x^713+624x^720+41472x^722+552x^729+536x^738+496x^747+296x^756+248x^765+176x^774+80x^783+56x^792+16x^801

The gray image is a linear code over GF(9) with n=810, k=5 and d=684.
This code was found by Heurico 1.16 in 2.01 seconds.