The generator matrix

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

generates a code of length 55 over Z3[X]/(X^2) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+48x^87+6x^89+148x^90+24x^92+308x^93+270x^95+542x^96+1020x^98+866x^99+2196x^101+1318x^102+4164x^104+2486x^105+7176x^107+3228x^108+8568x^110+3812x^111+7944x^113+2966x^114+4992x^116+1986x^117+2334x^119+862x^120+582x^122+514x^123+90x^125+298x^126+170x^129+82x^132+32x^135+10x^138+4x^141+2x^144

The gray image is a linear code over GF(3) with n=165, k=10 and d=87.
This code was found by Heurico 1.16 in 43.6 seconds.