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.