The generator matrix

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

generates a code of length 57 over Z3[X]/(X^2) who´s minimum homogenous weight is 107.

Homogenous weight enumerator: w(x)=1x^0+240x^107+156x^108+342x^110+206x^111+330x^113+110x^114+174x^116+112x^117+138x^119+56x^120+126x^122+62x^123+72x^125+8x^126+24x^128+6x^129+12x^131+6x^132+2x^135+2x^138+2x^141

The gray image is a linear code over GF(3) with n=171, k=7 and d=107.
This code was found by Heurico 1.13 in 0.0572 seconds.