The generator matrix

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

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+606x^41+534x^42+1728x^43+2586x^44+1946x^45+3672x^46+3834x^47+1936x^48+1728x^49+1050x^50+18x^51+24x^53+18x^54+2x^57

The gray image is a linear code over GF(3) with n=207, k=9 and d=123.
This code was found by Heurico 1.16 in 0.25 seconds.