The generator matrix

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

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+72x^36+220x^39+24x^40+396x^42+372x^43+656x^45+1746x^46+1772x^48+5100x^49+3790x^51+9750x^52+5246x^54+11376x^55+4464x^57+8322x^58+2004x^60+2676x^61+546x^63+338x^66+120x^69+40x^72+10x^75+8x^78

The gray image is a linear code over GF(3) with n=81, k=10 and d=36.
This code was found by Heurico 1.16 in 13 seconds.