The generator matrix

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

generates a code of length 22 over Z3[X]/(X^2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+1130x^36+2550x^39+4548x^42+6156x^45+4200x^48+1014x^51+80x^54+4x^63

The gray image is a linear code over GF(3) with n=66, k=9 and d=36.
This code was found by Heurico 1.16 in 12.9 seconds.