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 1 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 2X+1 X+1 1 2X+2 2X+2 2X+2 1 1 1 0 0 X 2X+1 2X+1 X+1 X X+1 0 X 2X+1 X+1 2X 2X 2 1 1 2 X+2 0
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 2X 0 X 0 X 2X 0 X 2X 0 X 2X 2X X 0 X X 2X 0 0 2X 0 X 0 X 2X 2X X 2X
generates a code of length 56 over Z3[X]/(X^2) who´s minimum homogenous weight is 109.
Homogenous weight enumerator: w(x)=1x^0+36x^109+48x^111+90x^112+26x^114+36x^115+2x^117+2x^132+2x^141
The gray image is a linear code over GF(3) with n=168, k=5 and d=109.
This code was found by Heurico 1.16 in 0.0179 seconds.