The generator matrix

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

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+74x^36+60x^37+114x^38+100x^39+708x^40+276x^41+2552x^42+3588x^43+6666x^44+9812x^45+6744x^46+12684x^47+9820x^48+4692x^49+588x^50+98x^51+246x^52+84x^53+88x^54+34x^57+14x^60+6x^63

The gray image is a linear code over GF(3) with n=207, k=10 and d=108.
This code was found by Heurico 1.16 in 2.5 seconds.