The generator matrix

 1  0  1  1  1  1 2X^2  1  1  1  1  X  1  1 2X^2+X  1 2X  1  1 2X  1  X  1
 0  1  1  2 2X^2+2X+1 2X^2  1  2 X+2 2X^2+2X+1 2X^2+X  1 2X^2+X+2 2X  1 2X^2+2X+1  1 2X+2  X  1 X+2  X 2X^2+X
 0  0 2X  0  0 2X^2+X 2X^2+X 2X  X 2X 2X^2+2X X^2+X 2X^2+2X 2X^2 2X^2+2X X^2 X^2 X^2+2X 2X^2+X  0 2X^2+X X^2+X 2X
 0  0  0 X^2  0 X^2 2X^2  0 2X^2 2X^2 2X^2  0 X^2 X^2  0  0 2X^2 X^2 2X^2 X^2 2X^2  0  0
 0  0  0  0 2X^2  0 2X^2 X^2  0  0 2X^2 X^2  0 2X^2 X^2 X^2 2X^2 2X^2 X^2 2X^2 2X^2 2X^2 2X^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+264x^38+386x^39+432x^40+1068x^41+2450x^42+2592x^43+8094x^44+7986x^45+6642x^46+14772x^47+8056x^48+3456x^49+1830x^50+710x^51+204x^53+68x^54+12x^56+16x^57+8x^60+2x^66

The gray image is a linear code over GF(3) with n=207, k=10 and d=114.
This code was found by Heurico 1.16 in 92.3 seconds.