The generator matrix

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

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+1260x^27+4716x^30+12258x^33+20328x^36+15804x^39+4374x^42+306x^45+2x^54

The gray image is a linear code over GF(3) with n=54, k=10 and d=27.
This code was found by Heurico 1.16 in 62.7 seconds.