The generator matrix

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

generates a code of length 23 over Z3[X]/(X^3) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+92x^36+474x^39+162x^40+1012x^42+972x^43+2916x^44+1904x^45+1944x^46+5832x^47+2010x^48+1296x^49+862x^51+136x^54+54x^57+16x^60

The gray image is a linear code over GF(3) with n=207, k=9 and d=108.
This code was found by Heurico 1.16 in 0.577 seconds.