The generator matrix

 1  0  1  1  1  1  1  0  1
 0  1  1  2  0 2X+1  2  1  0
 0  0 2X  0  0 2X 2X  X  0
 0  0  0  X  0 2X  0 2X 2X
 0  0  0  0  X 2X  X 2X  X

generates a code of length 9 over Z3[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+54x^12+162x^14+180x^15+648x^17+240x^18+648x^20+216x^21+36x^24+2x^27

The gray image is a linear code over GF(3) with n=27, k=7 and d=12.
This code was found by Heurico 1.16 in 0.00431 seconds.