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

generates a code of length 27 over F9[X]/(X^2) who´s minimum homogenous weight is 207.

Homogenous weight enumerator: w(x)=1x^0+384x^207+648x^208+168x^216+5184x^217+120x^234+56x^243

The gray image is a linear code over GF(9) with n=243, k=4 and d=207.
This code was found by Heurico 1.16 in 1.9 seconds.