The generator matrix

 1  0  0  1  1  1  1  1  1 2X  1  1  1  X 2X  1  1  X  1  1 2X 2X  1  1  1  1  X  0  1 2X  1  1  1 2X  1  X  1  1  1  1  1  1  X  X  1  1  1  1  0  0  1  1  1  1  1  0  1
 0  1  0 2X  1 2X+1  2  0 X+2  1 2X+2 2X+1 X+2  1  1 X+1  X  1  2  1  1  0  2 2X 2X+2  X  1  1 2X  1  0 X+2 2X+1  X  X  1 2X+2 2X+1  X 2X+2 X+1  1  1  X  2 X+1  1 X+2  1 2X  X  0 2X  X 2X  1 2X+1
 0  0  1 2X+1  1 2X 2X+2  2  X  1 X+2  2 X+1  X 2X+2 X+1 2X+1  1 X+2  2 X+2  1  X  1 X+1  2  0 X+2  0 X+1 X+2 2X+1 X+1  1  1 X+1  2 X+2 2X+2  1 X+2 2X+1 2X+2  1 2X 2X+2 2X+2  0  X  1 2X 2X+1 X+2  X 2X+2  1  X

generates a code of length 57 over Z3[X]/(X^2) who´s minimum homogenous weight is 110.

Homogenous weight enumerator: w(x)=1x^0+120x^110+120x^111+204x^113+66x^114+108x^116+18x^117+24x^119+16x^120+18x^122+6x^123+2x^126+2x^129+12x^131+12x^132

The gray image is a linear code over GF(3) with n=171, k=6 and d=110.
This code was found by Heurico 1.16 in 0.0329 seconds.