The generator matrix

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

generates a code of length 18 over Z3[X]/(X^2) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+104x^27+126x^30+450x^33+768x^36+558x^39+90x^42+72x^45+18x^48

The gray image is a linear code over GF(3) with n=54, k=7 and d=27.
This code was found by Heurico 1.16 in 2.97 seconds.