The generator matrix

 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 a^2*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^7*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+80x^81+288x^90+5832x^96+144x^99+216x^108

The gray image is a linear code over GF(9) with n=108, k=4 and d=81.
This code was found by Heurico 1.16 in 0.00263 seconds.