The generator matrix

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

generates a code of length 81 over F9[X]/(X^2) who´s minimum homogenous weight is 629.

Homogenous weight enumerator: w(x)=1x^0+6552x^629+15424x^630+12600x^631+1440x^632+216x^633+1080x^636+30744x^638+60000x^639+30528x^640+3456x^641+1512x^642+1728x^645+48456x^647+73552x^648+37224x^649+3024x^650+4104x^651+3024x^654+60048x^656+90848x^657+42120x^658+3744x^659+8x^675+8x^702

The gray image is a linear code over GF(9) with n=729, k=6 and d=629.
This code was found by Heurico 1.16 in 41.5 seconds.