The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 X 0 2X
0 1 1 2 0 1 2 1 0 2X+1 2 1 2X+1 0 2 1 X 2X+1 2 1 2X+1 1 1 1
0 0 2X 0 0 0 0 0 0 0 0 0 0 X X 2X X X X X 2X 2X 2X 2X
0 0 0 X 0 0 0 0 X 2X X 2X X 2X 2X 0 0 X 2X 0 X 2X 0 0
0 0 0 0 X 0 0 X 2X 2X X X 0 2X 2X 2X 2X 2X 2X X 0 0 0 0
0 0 0 0 0 2X 0 2X X 0 X X 2X 2X X 2X 0 0 0 X 2X 0 0 2X
0 0 0 0 0 0 X 2X 0 2X 2X X X 2X 2X X 2X X X X 2X 2X 2X 0
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+178x^36+132x^38+234x^39+684x^41+666x^42+2106x^44+1242x^45+4128x^47+1764x^48+4068x^50+1404x^51+1836x^53+782x^54+168x^56+162x^57+90x^60+38x^63
The gray image is a linear code over GF(3) with n=72, k=9 and d=36.
This code was found by Heurico 1.16 in 8.03 seconds.