The generator matrix

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

generates a code of length 27 over Z3[X]/(X^3) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+174x^47+558x^48+2160x^49+2928x^50+2890x^51+7146x^52+7290x^53+7514x^54+13008x^55+7584x^56+3726x^57+2880x^58+924x^59+112x^60+72x^61+54x^62+18x^63+6x^64+4x^69

The gray image is a linear code over GF(3) with n=243, k=10 and d=141.
This code was found by Heurico 1.16 in 2.64 seconds.