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.