The generator matrix

 1  0  0  0  1  1  1 2X^2 2X^2+2X  1  1 2X^2 2X  1  1  1  1  1  1  1  1  1  1
 0  1  0  0 2X^2 X^2  X X^2+2X  1 X+1 X^2+X+1  1  1 X+2 X+2 X^2+X+2  2 X^2+X X^2+1 2X^2+X+1 X^2+2X+1 2X^2+1  1
 0  0  1  0 2X^2+2X+1 2X^2+X  2  1 2X^2+2X+1 2X^2+2X+2 X^2+1 X+2 2X^2+2X 2X^2 X+1 2X^2+2X 2X+2 2X^2+X+1  X 2X+1 2X^2+2 2X^2+2X+2 2X^2
 0  0  0  1 2X^2+2X+2 2X^2+X+2 2X+1  1 2X^2+2 X+1 X+2  X 2X+2  2 2X^2+2X+1 X^2+1 2X+2 2X^2 X^2+X+1  1 X+2 X^2+2X 2X^2+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+942x^38+1804x^39+5790x^40+10272x^41+21698x^42+27258x^43+64782x^44+66164x^45+84726x^46+117930x^47+68790x^48+37644x^49+17304x^50+5500x^51+570x^52+162x^53+66x^54+18x^55+18x^56+2x^57

The gray image is a linear code over GF(3) with n=207, k=12 and d=114.
This code was found by Heurico 1.16 in 147 seconds.