The generator matrix

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

generates a code of length 27 over Z3[X]/(X^3) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+486x^46+1278x^47+1996x^48+4290x^49+8814x^50+8362x^51+17970x^52+26730x^53+26340x^54+31218x^55+26934x^56+11930x^57+6996x^58+3156x^59+206x^60+228x^61+144x^62+2x^63+48x^64+12x^65+6x^66

The gray image is a linear code over GF(3) with n=243, k=11 and d=138.
This code was found by Heurico 1.16 in 22.7 seconds.