The generator matrix

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

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+44x^12+180x^14+182x^15+648x^17+242x^18+594x^20+244x^21+36x^23+16x^24

The gray image is a linear code over GF(3) with n=27, k=7 and d=12.
This code was found by Heurico 1.13 in 0.0016 seconds.