The generator matrix

 1  0  1  1  1  1  1 2X^2+X  1  1  1 2X  1  1  0  1  1  1  1 2X^2+X  1  1  0  1 X^2  1  1
 0  1 2X^2+2X+1  2 2X^2+X X+1 2X^2+X+2  1 2X 2X+2 2X^2+1  1 X+1 2X^2+X  1  2 2X^2+X+2 2X^2+2X+1  2  1 X^2+2 2X^2+X+2  1 X^2+X+2  1 2X^2+2X+1 X^2+2X+1
 0  0 2X^2  0 2X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 2X^2  0 2X^2 X^2 2X^2  0 2X^2 X^2 2X^2 X^2 2X^2 2X^2  0  0
 0  0  0 X^2 2X^2 2X^2 X^2  0 X^2 2X^2  0 2X^2 X^2  0 X^2 2X^2  0 X^2  0 X^2 2X^2 X^2 2X^2  0 2X^2  0 X^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+378x^49+162x^50+140x^51+1374x^52+648x^53+26x^54+2628x^55+648x^56+450x^58+74x^60+30x^61+2x^69

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 18.8 seconds.