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

generates a code of length 27 over F9[X]/(X^2) who´s minimum homogenous weight is 171.

Homogenous weight enumerator: w(x)=1x^0+280x^171+1680x^180+3416x^189+5672x^198+5832x^200+9256x^207+93312x^209+13656x^216+373248x^218+13776x^225+8720x^234+2592x^243

The gray image is a linear code over GF(9) with n=243, k=6 and d=171.
This code was found by Heurico 1.16 in 34.2 seconds.