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.