The generator matrix

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

generates a code of length 23 over Z3[X]/(X^3) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+102x^38+148x^39+504x^40+444x^41+614x^42+888x^43+1998x^44+1804x^45+5298x^46+3480x^47+1714x^48+1278x^49+654x^50+262x^51+264x^52+108x^53+70x^54+30x^55+18x^56+4x^57

The gray image is a linear code over GF(3) with n=207, k=9 and d=114.
This code was found by Heurico 1.16 in 0.545 seconds.