The generator matrix

 1  0  0  0  1  1  1 2X  1  1  1  1 2X  0  1  X  1  1  1  1  0  1
 0  1  0  0 2X  1 2X+1  1  0 2X  1 X+1  1  1 X+1  1  1 2X+2 X+2 2X+1  1  X
 0  0  1  0 2X+1  1 2X+2 X+1  X  2 X+2  X  X 2X+2 2X+1  1  0 2X+2 2X  1 2X 2X
 0  0  0  1 2X+2  X X+2 X+2  1  2 2X+1 2X  1 X+2 X+2  1 X+1 2X+1 2X 2X+1  2  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+148x^36+114x^37+180x^38+592x^39+306x^40+312x^41+896x^42+342x^43+450x^44+930x^45+426x^46+378x^47+846x^48+216x^49+120x^50+220x^51+54x^52+18x^53+10x^54+2x^57

The gray image is a linear code over GF(3) with n=66, k=8 and d=36.
This code was found by Heurico 1.16 in 0.172 seconds.