The generator matrix

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

generates a code of length 23 over Z3[X]/(X^3) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+90x^41+316x^42+552x^43+510x^44+1026x^45+1500x^46+888x^47+940x^48+528x^49+114x^50+32x^51+12x^52+18x^53+30x^54+2x^57+2x^63

The gray image is a linear code over GF(3) with n=207, k=8 and d=123.
This code was found by Heurico 1.16 in 0.0388 seconds.