The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 X 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 1 1 1 0 1 1 1 2X X 0 1 1 1 1 1 2X 1 0 0 X 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 2 2X+1 1 1 X+2 0 2X+1 0 2X+1 2 1 0 2 2X+1 1 1 X X+1 X 2X+1 0 X 1 X+2 2 2X+1 1 1 1 2X+2 X X+2 X 0 1 2X+1 0 X X 2 0
0 0 2X 0 0 0 0 0 0 2X X 2X 2X 2X 2X 0 2X 0 2X 2X 0 2X 2X 0 2X 0 X 0 2X 0 X 0 X 2X X X 2X X 0 X X 2X 2X 2X 2X 0 0 X X X X 2X X 0
0 0 0 X 0 0 0 0 0 0 0 0 0 0 2X X 2X X 0 X X 2X 2X X 0 X X 0 X 0 X 0 2X X X 2X 0 0 2X X X X X 0 2X 2X 0 2X X X 0 X 2X 0
0 0 0 0 X 0 0 0 0 0 0 0 0 0 2X 2X X 0 2X X 2X 0 2X X 2X 0 2X 2X 0 2X 2X X 2X X X X 2X X 2X 2X 2X 0 0 2X 2X X 2X 2X 0 X 2X X X 0
0 0 0 0 0 2X 0 0 X 2X 2X X 2X 0 2X 2X 2X X 0 0 0 X X X 0 0 0 X 2X X 2X X 0 0 2X 0 X X 0 2X 2X X 2X 0 0 2X X X X X 0 0 0 X
0 0 0 0 0 0 X 0 X 0 X X X 2X 2X 0 X 2X 2X 0 2X X 2X 0 0 2X X 2X 0 2X 0 X 0 2X 2X 0 2X X 0 X 0 X X 0 2X X 0 X X X 2X X 2X 2X
0 0 0 0 0 0 0 X X X X 0 2X X 2X X X X X 2X 2X 2X X 0 X X 2X X X 0 0 0 0 2X 2X 2X 0 0 X 0 2X 0 X 0 2X 0 0 0 X 0 2X 2X 0 2X
generates a code of length 54 over Z3[X]/(X^2) who´s minimum homogenous weight is 87.
Homogenous weight enumerator: w(x)=1x^0+104x^87+308x^90+42x^91+48x^92+606x^93+216x^94+186x^95+1168x^96+408x^97+564x^98+2158x^99+954x^100+1242x^101+3426x^102+1848x^103+1884x^104+5390x^105+2418x^106+2904x^107+5950x^108+2808x^109+2916x^110+5544x^111+2280x^112+2082x^113+4186x^114+1374x^115+906x^116+2100x^117+570x^118+330x^119+1106x^120+192x^121+60x^122+400x^123+12x^124+190x^126+116x^129+36x^132+12x^135+2x^138+2x^141
The gray image is a linear code over GF(3) with n=162, k=10 and d=87.
This code was found by Heurico 1.16 in 43.5 seconds.