The generator matrix

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

generates a code of length 22 over Z3[X]/(X^2) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+464x^39+588x^42+492x^45+488x^48+150x^51+2x^54+2x^57

The gray image is a linear code over GF(3) with n=66, k=7 and d=39.
This code was found by Heurico 1.13 in 2.94 seconds.