The generator matrix

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

generates a code of length 22 over Z3[X]/(X^2) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+258x^37+510x^38+124x^39+510x^40+456x^41+220x^42+822x^43+822x^44+184x^45+750x^46+822x^47+164x^48+480x^49+264x^50+32x^51+96x^52+42x^53+4x^54

The gray image is a linear code over GF(3) with n=66, k=8 and d=37.
This code was found by Heurico 1.16 in 68.4 seconds.