The generator matrix

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

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+852x^49+606x^50+1302x^51+3726x^52+1302x^53+2492x^54+4926x^55+1260x^56+1296x^57+1650x^58+222x^59+12x^60+18x^61+12x^62+6x^64

The gray image is a linear code over GF(3) with n=243, k=9 and d=147.
This code was found by Heurico 1.16 in 0.301 seconds.