The generator matrix

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

generates a code of length 24 over Z3[X]/(X^2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+18x^36+152x^39+90x^40+90x^41+346x^42+144x^43+180x^44+726x^45+414x^46+540x^47+1068x^48+396x^49+450x^50+886x^51+342x^52+198x^53+338x^54+72x^55+54x^57+46x^60+6x^63+4x^66

The gray image is a linear code over GF(3) with n=72, k=8 and d=36.
This code was found by Heurico 1.16 in 0.181 seconds.