The generator matrix

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

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+184x^36+114x^37+252x^38+782x^39+588x^40+516x^41+1830x^42+744x^43+1086x^44+2906x^45+1284x^46+1332x^47+3256x^48+1104x^49+960x^50+1638x^51+462x^52+228x^53+298x^54+78x^55+28x^57+6x^60+4x^63+2x^66

The gray image is a linear code over GF(3) with n=69, k=9 and d=36.
This code was found by Heurico 1.16 in 1.73 seconds.