The generator matrix

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

generates a code of length 27 over Z3[X]/(X^3) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+452x^45+780x^46+4182x^47+7128x^48+9504x^49+25416x^50+33410x^51+49812x^52+78144x^53+83950x^54+85458x^55+79704x^56+44734x^57+16524x^58+9774x^59+2074x^60+210x^61+84x^62+50x^63+36x^64+12x^65+2x^66

The gray image is a linear code over GF(3) with n=243, k=12 and d=135.
This code was found by Heurico 1.16 in 180 seconds.