The generator matrix

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

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+830x^45+2310x^48+3822x^51+5018x^54+4926x^57+2334x^60+432x^63+10x^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 9.22 seconds.