The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 X 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 0
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 2 2X+1 1 1 X+2 0 2X+1 2 2X+1 1 0 2 2X+1 X 2X+1 2X+1 2 2X X+2 0 1 1 1
0 0 2X 0 0 0 0 0 0 2X X 2X 2X 2X 2X 0 2X 0 X 2X X 0 2X 0 2X 2X X 2X X 2X X 0 X 0 0 0
0 0 0 X 0 0 0 0 0 0 0 0 0 0 2X X 2X X 0 X 0 2X 2X X 2X X X 0 0 2X X 2X X X 0 X
0 0 0 0 X 0 0 0 0 0 0 0 0 0 2X 2X X 0 2X X 2X X 0 X X X 0 X X 0 X X 0 2X 2X X
0 0 0 0 0 2X 0 0 X 2X 2X X 2X 0 2X 2X 2X X X 0 0 2X 2X 0 2X 0 2X X X 0 2X 0 0 2X X X
0 0 0 0 0 0 X 0 X 0 X X X 2X 2X 0 X 2X 2X 0 2X X 2X 0 0 2X 0 0 2X 0 0 2X 0 2X 0 2X
0 0 0 0 0 0 0 X X X X 0 2X X 2X X X X 0 2X 0 X 0 0 0 X 2X 0 X 2X 2X 0 2X 2X 0 X
generates a code of length 36 over Z3[X]/(X^2) who´s minimum homogenous weight is 54.
Homogenous weight enumerator: w(x)=1x^0+144x^54+280x^57+872x^60+2162x^63+6380x^66+11120x^69+15388x^72+13152x^75+6900x^78+1898x^81+416x^84+220x^87+88x^90+22x^93+4x^96+2x^99
The gray image is a linear code over GF(3) with n=108, k=10 and d=54.
This code was found by Heurico 1.16 in 23.4 seconds.