The generator matrix

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

generates a code of length 27 over Z3[X]/(X^3) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+168x^49+162x^50+612x^51+1020x^52+432x^53+1656x^54+966x^55+540x^56+528x^57+390x^58+22x^60+42x^61+12x^63+6x^64+2x^69+2x^72

The gray image is a linear code over GF(3) with n=243, k=8 and d=147.
This code was found by Heurico 1.16 in 0.0476 seconds.