The generator matrix

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

generates a code of length 22 over Z3[X]/(X^2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+30x^36+60x^37+90x^38+60x^39+204x^40+180x^41+30x^42+258x^43+378x^44+36x^45+264x^46+288x^47+36x^48+174x^49+36x^50+24x^51+12x^52+14x^54+12x^57

The gray image is a linear code over GF(3) with n=66, k=7 and d=36.
This code was found by Heurico 1.16 in 0.0206 seconds.