The generator matrix

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

generates a code of length 22 over Z3[X]/(X^2) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+144x^31+228x^32+420x^33+1236x^34+1632x^35+1984x^36+4308x^37+5664x^38+5068x^39+10506x^40+13650x^41+11930x^42+18852x^43+21156x^44+15096x^45+18360x^46+16584x^47+8734x^48+9762x^49+5886x^50+2444x^51+2376x^52+810x^53+224x^54+66x^55+22x^57+2x^60+2x^63

The gray image is a linear code over GF(3) with n=66, k=11 and d=31.
This code was found by Heurico 1.16 in 102 seconds.