The generator matrix

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

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+280x^684+72x^685+792x^692+1880x^693+792x^694+2880x^695+15912x^701+8944x^702+4176x^703+10512x^704+38232x^710+19104x^711+11160x^712+22464x^713+105912x^719+42640x^720+19944x^721+40320x^722+101592x^728+36912x^729+16344x^730+28800x^731+480x^738+360x^747+328x^756+296x^765+184x^774+48x^783+72x^792+8x^801

The gray image is a linear code over GF(9) with n=810, k=6 and d=684.
This code was found by Heurico 1.16 in 53.7 seconds.