The generator matrix
1 0 1 1 1 1 1 0 1 1 1 X 1 1 1 X 1 1 1 0 1 1 1 X 1 1 1 1 1 1 1 1 1 2X 2X 2X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 X 0 X X 2X 1 X 0 X X 2X 0 1
0 1 1 2 2X+1 0 2 1 X 2X+1 X+2 1 X X+1 X+2 1 X+1 0 2 1 X 1 X+2 1 2X 2X 2X+1 X+1 2X 1 2X+2 2X+2 2X+2 1 1 1 0 0 X 2X+1 2X+1 X+1 2 2 X+2 X X+1 X+2 X 0 2X+1 X+1 2 X+2 X X 0 1 1 X 1 2X 0 1 X 1 1 X 1
0 0 2X 0 X X 2X 2X 2X 0 X X X 2X 2X 2X X 2X X X 0 0 0 0 0 X 2X 0 2X X 0 X 2X 0 X 2X 0 X 2X 2X X 0 0 X 2X X X 0 0 2X 0 2X 2X X X 2X X 0 0 X 0 0 2X X 2X X X 0 2X
generates a code of length 69 over Z3[X]/(X^2) who´s minimum homogenous weight is 136.
Homogenous weight enumerator: w(x)=1x^0+90x^136+48x^137+12x^138+48x^140+8x^141+12x^142+12x^143+2x^144+4x^150+6x^151
The gray image is a linear code over GF(3) with n=207, k=5 and d=136.
This code was found by Heurico 1.16 in 0.164 seconds.