The generator matrix

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

generates a code of length 27 over Z3[X]/(X^2) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+846x^45+2370x^48+3546x^51+5336x^54+4800x^57+2340x^60+426x^63+12x^66+6x^72

The gray image is a linear code over GF(3) with n=81, k=9 and d=45.
This code was found by Heurico 1.16 in 9.51 seconds.