The generator matrix
1 0 0 1 1 1 1 1 0 2X 1 1 1 X 1 1 1 1 1 1 0 1 0 1 1 X 1 2X 2X 1 1 0 1 1 1 1 2X 1 2X 1 X 1 1 0 1 1 0 0 1 1 X 1 2X 1 1 0
0 1 0 1 0 2 1 2 1 1 0 2X+1 2X+2 1 0 2X+1 2X 2 2X+2 0 2X 2X+1 1 1 2 1 2X 1 1 2 0 1 1 X+2 X+2 X+1 1 2X+1 1 0 1 2X+1 2X 1 X+2 1 1 2X X+1 1 1 2X 1 X+1 0 X
0 0 1 2 1 2 1 0 2 2X+1 2 2X 2X+1 1 0 2X+2 1 2 2X+1 X+2 1 2X X X+1 0 2 2X X+2 0 X X+1 2X+1 X+2 2 X+1 0 2X+1 2X+2 1 X+1 1 X+1 2X X+2 2 2X 1 1 2X 2X+1 2 X X+2 X+2 2X+2 0
0 0 0 2X 0 0 0 0 0 0 0 0 2X 0 0 X 2X X X X X 2X 2X 0 2X 2X 2X 0 X X X 0 X 2X 2X 0 2X 2X 2X 0 X 2X 0 2X X 0 X X 2X 0 2X 2X 0 2X X X
0 0 0 0 2X 0 0 0 0 0 X 2X 0 0 X X 2X 0 X 2X 0 X X 2X X X 2X 2X 0 2X X 2X 2X X 0 0 2X 0 2X 2X X 2X X 0 X 2X 2X 2X 2X X 2X 0 X 2X 2X X
0 0 0 0 0 X 0 X X 2X X 2X 2X 0 2X X 2X 0 0 X 0 0 2X X 0 0 2X 0 0 X X 0 2X 2X X 2X 2X X 0 0 2X 0 2X 2X 2X 2X 0 2X 0 0 X 2X 0 X 0 X
0 0 0 0 0 0 X X X X 0 0 2X 2X X 0 X X 2X 2X 2X X 0 X 0 0 0 0 X X 0 X X X 0 0 X 0 0 2X 2X X 2X X X 2X X X 0 X 0 X 0 X 0 0
generates a code of length 56 over Z3[X]/(X^2) who´s minimum homogenous weight is 94.
Homogenous weight enumerator: w(x)=1x^0+30x^94+42x^95+370x^96+150x^97+204x^98+984x^99+426x^100+540x^101+1938x^102+870x^103+1056x^104+3034x^105+1506x^106+1596x^107+4810x^108+2004x^109+2496x^110+5862x^111+2706x^112+2658x^113+6136x^114+2466x^115+2226x^116+4820x^117+1644x^118+1470x^119+2810x^120+876x^121+618x^122+1358x^123+354x^124+186x^125+460x^126+84x^127+30x^128+122x^129+56x^132+6x^133+20x^135+14x^138+8x^141+2x^144
The gray image is a linear code over GF(3) with n=168, k=10 and d=94.
This code was found by Heurico 1.16 in 72.5 seconds.