The generator matrix

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

generates a code of length 23 over Z3[X]/(X^3) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+182x^39+522x^40+1506x^41+2334x^42+3132x^43+6618x^44+7866x^45+10254x^46+12096x^47+7754x^48+3978x^49+2094x^50+528x^51+90x^52+42x^53+44x^54+6x^55+2x^57

The gray image is a linear code over GF(3) with n=207, k=10 and d=117.
This code was found by Heurico 1.16 in 2.14 seconds.