The generator matrix

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

generates a code of length 23 over Z3[X]/(X^2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+72x^36+60x^37+114x^38+100x^39+222x^40+276x^41+120x^42+672x^43+834x^44+104x^45+912x^46+1020x^47+96x^48+804x^49+588x^50+96x^51+246x^52+84x^53+82x^54+36x^57+18x^60+2x^63+2x^66

The gray image is a linear code over GF(3) with n=69, k=8 and d=36.
This code was found by Heurico 1.16 in 0.209 seconds.