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  X  0  0 2X  X  X  0  X 2X 2X  0  0
 0  0  X  0  0  0  0  0  0 2X  X  X  X  X 2X  X  X  X  X 2X  0  0
 0  0  0  X  0  0  0  0  X 2X  0 2X 2X 2X  0  X 2X  0 2X  X 2X  0
 0  0  0  0  X  0  0  0 2X 2X  0 2X  X 2X 2X 2X  0 2X 2X  0 2X  0
 0  0  0  0  0  X  0  0 2X 2X  X 2X  0  0 2X  X 2X  X 2X  0  0  0
 0  0  0  0  0  0  X  0 2X  0 2X  0 2X  0 2X 2X  X  X  X  X  X  0
 0  0  0  0  0  0  0  X 2X  0  X  X 2X 2X  X 2X  0  0  0  0  X  0

generates a code of length 22 over Z3[X]/(X^2) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+78x^27+202x^30+382x^33+502x^36+776x^39+1014x^42+13122x^44+1146x^45+1086x^48+660x^51+446x^54+200x^57+50x^60+14x^63+4x^66

The gray image is a linear code over GF(3) with n=66, k=9 and d=27.
This code was found by Heurico 1.16 in 1.64 seconds.