The generator matrix

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

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+1044x^36+2826x^39+4320x^42+6048x^45+4410x^48+972x^51+56x^54+6x^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 70.3 seconds.