The generator matrix

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

generates a code of length 12 over F9[X]/(X^2) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+320x^81+5832x^88+1728x^90+46656x^97+4320x^99+192x^108

The gray image is a linear code over GF(9) with n=108, k=5 and d=81.
This code was found by Heurico 1.16 in 0.0598 seconds.