The generator matrix

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

generates a code of length 56 over Z3[X]/(X^2) who´s minimum homogenous weight is 97.

Homogenous weight enumerator: w(x)=1x^0+192x^97+318x^98+472x^99+894x^100+1134x^101+1034x^102+1686x^103+1980x^104+1450x^105+2526x^106+2748x^107+2024x^108+3390x^109+3852x^110+2860x^111+3894x^112+4068x^113+3036x^114+3990x^115+3618x^116+2260x^117+2868x^118+2484x^119+1388x^120+1602x^121+1200x^122+636x^123+654x^124+408x^125+128x^126+156x^127+54x^128+8x^129+18x^130+6x^131+8x^132+2x^144+2x^147

The gray image is a linear code over GF(3) with n=168, k=10 and d=97.
This code was found by Heurico 1.16 in 41.2 seconds.