The generator matrix

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

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+162x^38+192x^39+534x^40+1230x^41+2310x^42+2232x^43+7992x^44+7542x^45+8664x^46+14862x^47+7686x^48+3012x^49+1812x^50+390x^51+126x^52+180x^53+98x^54+12x^55+6x^56+6x^57

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 2.63 seconds.