The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  1
 0  X 2X  0 2X^2+X 2X  0 2X^2+X 2X X^2 2X^2+X 2X 2X^2+X  X  0 X^2+2X X^2+X 2X^2+X X^2 2X^2+2X 2X^2+X  0
 0  0 X^2  0  0  0 X^2 2X^2 X^2 X^2 2X^2 X^2 X^2  0 X^2  0  0 2X^2 2X^2 X^2  0  0
 0  0  0 X^2  0 X^2 X^2 2X^2 X^2  0 X^2 2X^2  0  0 2X^2 X^2 X^2 2X^2 X^2 X^2 2X^2  0
 0  0  0  0 2X^2 2X^2 X^2 2X^2 2X^2 X^2 2X^2  0  0 X^2  0 X^2  0 2X^2  0 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+74x^36+54x^38+210x^39+216x^40+72x^41+252x^42+864x^43+3132x^44+332x^45+864x^46+108x^47+234x^48+36x^50+84x^51+16x^54+6x^57+6x^60

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 0.0687 seconds.