The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 X 1 1 1 0 1 1 1 1 0 1 1 1 1 2X 1 1 1 1 1 1 1 2X 1 0 1 0 1 2X 1 1 1 X 1 1 1 1 1 X 1 1 2X 1 2X 0 0 1 1 2X 1 0 1 2X 1 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 X+1 X+2 1 1 0 2X+1 2 1 0 2X+2 2X+1 X 1 2X+1 2 X 2 1 X+1 2 X 1 2X+2 2X+1 2X+2 1 1 1 0 1 X+1 1 2X 2X+1 2X+1 1 X+2 2X 2X+2 2X+1 0 1 X+2 X 1 X 1 1 1 2X+2 2 1 X+2 1 2X+1 1 2X+2 X+2 0
0 0 2X 0 0 0 0 0 0 0 0 0 0 X 0 X 2X X 2X X 0 X 2X X 2X 2X X 0 X 0 2X 2X 2X 0 2X X X X 2X X 0 0 2X 0 X X X X X 2X X 2X 2X X 2X 2X 2X 0 0 X 2X 0 0 0 0 0 X 2X 2X 2X 0 X
0 0 0 X 0 0 0 0 0 0 0 2X 0 0 2X X 2X 0 X 2X 2X X X X X 0 2X X X X 0 X 2X 2X 0 X 2X X 0 2X 2X 2X X 2X 0 0 0 0 X X X X 0 X 2X 2X 2X 0 X X 0 0 2X 2X 0 X 0 0 X 2X X 2X
0 0 0 0 X 0 0 0 X 2X 2X 0 X 2X 2X 0 0 2X 0 X X 2X X 0 0 0 X 2X X 2X 0 0 X 2X 2X 2X 0 2X 2X 0 0 0 X 0 0 X 0 2X X X 2X X 0 2X 2X X 2X 0 0 2X 2X X X 2X 2X X 0 X X 0 X X
0 0 0 0 0 2X 0 X 2X 2X 2X 2X 0 X 2X 2X 2X 0 2X 0 0 2X 2X 0 2X 0 0 X 0 2X X X 0 0 0 2X X 2X 2X 2X 2X 0 2X 2X 0 2X 2X 2X X 2X X X 0 X 2X 2X 0 X 2X 2X 2X 0 0 X X 0 X X 2X X 2X 2X
0 0 0 0 0 0 X 2X 2X 2X 0 2X 2X 2X X 2X 0 2X 2X 2X X 2X 2X 0 X X 0 2X 0 0 0 2X 2X X 0 X 2X 0 2X 0 X X 2X 0 0 X 2X X X X 0 0 2X X X 2X 2X X X 2X X 2X X 2X 0 X X 0 X 0 X X
generates a code of length 72 over Z3[X]/(X^2) who´s minimum homogenous weight is 126.
Homogenous weight enumerator: w(x)=1x^0+70x^126+12x^127+236x^129+180x^130+394x^132+624x^133+664x^135+1164x^136+640x^138+1530x^139+862x^141+2328x^142+890x^144+2658x^145+912x^147+2340x^148+780x^150+1410x^151+484x^153+702x^154+246x^156+162x^157+138x^159+12x^160+106x^162+58x^165+36x^168+22x^171+14x^174+4x^177+4x^180
The gray image is a linear code over GF(3) with n=216, k=9 and d=126.
This code was found by Heurico 1.16 in 8.02 seconds.