The generator matrix

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

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+318x^38+512x^39+1956x^40+3618x^41+7416x^42+8826x^43+18852x^44+25104x^45+31692x^46+33294x^47+25600x^48+12174x^49+5958x^50+1306x^51+246x^52+156x^53+80x^54+24x^55+12x^56+2x^60

The gray image is a linear code over GF(3) with n=207, k=11 and d=114.
This code was found by Heurico 1.16 in 18.2 seconds.