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

generates a code of length 27 over Z3[X]/(X^2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+50x^36+184x^39+378x^42+448x^45+702x^48+1458x^50+878x^51+5832x^53+1060x^54+5832x^56+1034x^57+836x^60+540x^63+274x^66+122x^69+34x^72+20x^75

The gray image is a linear code over GF(3) with n=81, k=9 and d=36.
This code was found by Heurico 1.16 in 2.7 seconds.