The generator matrix

 1  0  0  1  1  1  1  1  0  1  1  1 2X  1  1  1  X  1  1 2X  1  1  1
 0  1  0  1  0  2  1  2  1  0 2X+2 2X+1  1 2X  2  X  1  1 2X+1  1 2X  1 X+1
 0  0  1  2  1  2  1  0  2  2 2X+1 2X 2X+1 X+1  X 2X+2 X+2  X  2 X+1  X  X  1
 0  0  0 2X  0  0  0  0  0  X 2X  X 2X 2X  X 2X 2X 2X  X  X  X  X  X
 0  0  0  0 2X  0  X  X  X 2X 2X 2X  X 2X 2X 2X 2X  X 2X  0  X  0  X
 0  0  0  0  0  X  X  0 2X  X  X  X 2X  0 2X 2X  X  0  0 2X  0  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+236x^36+84x^37+282x^38+888x^39+372x^40+408x^41+1688x^42+912x^43+1218x^44+2948x^45+1482x^46+1284x^47+3092x^48+1140x^49+942x^50+1598x^51+384x^52+240x^53+406x^54+68x^57+8x^60+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 55.8 seconds.