The generator matrix

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

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+54x^46+162x^47+440x^48+324x^49+732x^50+1704x^51+1584x^52+2832x^53+2938x^54+2808x^55+2880x^56+2398x^57+540x^58+150x^59+12x^60+36x^61+48x^62+2x^63+22x^66+12x^69+2x^72+2x^75

The gray image is a linear code over GF(3) with n=243, k=9 and d=138.
This code was found by Heurico 1.16 in 21.1 seconds.