The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  X  0  0  0  0  0  0  0  X 2X 2X 2X  X 2X 2X  0  X 2X 2X 2X  0
 0  0  X  0  0  0  0  X 2X 2X  0  X 2X 2X  0 2X 2X  0  X 2X 2X  0
 0  0  0  X  0  0  X 2X  0  0  0 2X 2X 2X 2X  X 2X 2X  0  X 2X  0
 0  0  0  0  X  0 2X 2X  X 2X 2X 2X 2X 2X  X 2X  0  0  0  0  X  0
 0  0  0  0  0  X 2X 2X 2X 2X 2X  X  X  X 2X  X 2X 2X 2X 2X  X  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+222x^36+40x^39+90x^42+1458x^44+72x^45+120x^48+72x^51+110x^54+2x^66

The gray image is a linear code over GF(3) with n=66, k=7 and d=36.
This code was found by Heurico 1.16 in 0.663 seconds.