The generator matrix

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

generates a code of length 18 over Z3[X]/(X^3) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+564x^28+720x^29+3848x^30+6714x^31+19188x^32+22066x^33+64644x^34+70104x^35+108486x^36+120594x^37+71550x^38+29488x^39+11484x^40+1692x^41+126x^42+120x^43+42x^44+8x^45+2x^51

The gray image is a linear code over GF(3) with n=162, k=12 and d=84.
This code was found by Heurico 1.16 in 103 seconds.