The generator matrix
1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 0 X 1 1 1 0 1 1 X 1 1 1 1 1 0 1 1 1 1 1 X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 1 1 1
0 1 1 2 0 1 2 1 2X+1 1 0 2 X+2 2X+1 0 1 1 0 2 2X+1 1 2 2X+1 1 X 2 2X 2X+1 X 1 2X+2 X 2X+1 X+2 0 1 2X+2 X+2 X+2 2 1 X+1 X+1 0 0 X 0 X X 1 1 1 1 1 X X 2X+1
0 0 2X 0 0 0 0 0 0 0 2X X X 2X 2X 2X 2X 2X 2X 0 X X 0 0 X 2X X 0 2X X 0 0 X 2X 2X 2X 0 X X 0 X 2X X 2X 0 0 0 X X X 2X X X 0 X 2X 0
0 0 0 X 0 0 0 X 2X X 0 2X X 2X 2X 0 2X 2X 0 X 2X X 2X X 0 2X X X 2X X X X 2X 0 2X 0 X 0 2X 0 0 2X 0 0 0 2X 2X 0 2X 2X X 2X X X X 0 0
0 0 0 0 X 0 X X X X X 2X 0 X X 0 2X 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X X 0 2X 2X 2X X 2X 2X X 0 2X X 2X 0 2X 2X 2X 0 0 X 0 X 0 2X 2X X 2X 2X
0 0 0 0 0 2X 2X 0 2X X 0 2X X X 2X 2X X X 2X 2X 0 0 X 0 0 2X X 2X X 0 X X X 2X 0 2X X 2X X 0 0 0 2X 0 2X 0 X X 0 0 2X 2X X 2X 2X X X
generates a code of length 57 over Z3[X]/(X^2) who´s minimum homogenous weight is 102.
Homogenous weight enumerator: w(x)=1x^0+134x^102+18x^103+66x^104+374x^105+192x^106+132x^107+526x^108+186x^109+210x^110+488x^111+216x^112+366x^113+654x^114+372x^115+342x^116+538x^117+240x^118+222x^119+520x^120+198x^121+108x^122+218x^123+30x^124+12x^125+104x^126+6x^127+22x^129+24x^132+24x^135+4x^138+8x^141+4x^144+2x^147
The gray image is a linear code over GF(3) with n=171, k=8 and d=102.
This code was found by Heurico 1.16 in 0.676 seconds.