The generator matrix

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

generates a code of length 23 over Z3[X]/(X^3) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+132x^42+78x^43+222x^44+106x^45+1008x^46+420x^47+100x^48+24x^49+6x^50+24x^51+18x^52+40x^54+6x^55+2x^66

The gray image is a linear code over GF(3) with n=207, k=7 and d=126.
This code was found by Heurico 1.16 in 0.0293 seconds.