The generator matrix

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

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+96x^45+180x^46+144x^47+336x^48+426x^49+600x^50+760x^51+3054x^52+1650x^53+2630x^54+5718x^55+1674x^56+964x^57+654x^58+246x^59+206x^60+132x^61+60x^62+88x^63+42x^64+14x^66+6x^69+2x^72

The gray image is a linear code over GF(3) with n=243, k=9 and d=135.
This code was found by Heurico 1.16 in 0.674 seconds.