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^2  0  0  0  0  0  0  0 X^2 2X^2 2X^2 2X^2 X^2 2X^2 2X^2  0 X^2 2X^2 2X^2 2X^2  0
 0  0 X^2  0  0  0  0 X^2 2X^2 2X^2  0 X^2 2X^2 2X^2  0 2X^2 2X^2  0 X^2 2X^2 2X^2  0
 0  0  0 X^2  0  0 X^2 2X^2  0  0  0 2X^2 2X^2 2X^2 2X^2 X^2 2X^2 2X^2  0 X^2 2X^2  0
 0  0  0  0 X^2  0 2X^2 2X^2 X^2 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 2X^2  0  0  0  0 X^2  0
 0  0  0  0  0 X^2 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 X^2 X^2 2X^2 X^2 2X^2 2X^2 2X^2 2X^2 X^2 X^2

generates a code of length 22 over Z3[X]/(X^3) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+222x^36+40x^39+90x^42+5832x^44+72x^45+120x^48+72x^51+110x^54+2x^66

The gray image is a linear code over GF(3) with n=198, k=8 and d=108.
This code was found by Heurico 1.16 in 1.56 seconds.