The generator matrix

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

generates a code of length 52 over Z3[X]/(X^2) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+90x^87+84x^88+156x^89+404x^90+294x^91+828x^92+892x^93+630x^94+1614x^95+1672x^96+1362x^97+2844x^98+2368x^99+1914x^100+4494x^101+3416x^102+2454x^103+5628x^104+4054x^105+2694x^106+5040x^107+3268x^108+1950x^109+3414x^110+1980x^111+1176x^112+1722x^113+998x^114+450x^115+438x^116+326x^117+108x^118+66x^119+122x^120+6x^121+40x^123+30x^126+16x^129+4x^132+2x^135

The gray image is a linear code over GF(3) with n=156, k=10 and d=87.
This code was found by Heurico 1.16 in 36.3 seconds.