The generator matrix

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

generates a code of length 27 over Z3[X]/(X^3) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+40x^42+48x^43+6x^44+162x^45+114x^46+60x^47+358x^48+192x^49+240x^50+604x^51+4668x^52+480x^53+1158x^54+9036x^55+480x^56+940x^57+348x^58+192x^59+202x^60+144x^61+106x^63+30x^64+52x^66+18x^69+4x^72

The gray image is a linear code over GF(3) with n=243, k=9 and d=126.
This code was found by Heurico 1.16 in 0.7 seconds.