The generator matrix

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

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+228x^87+324x^88+570x^89+1180x^90+1194x^91+1752x^92+2960x^93+2832x^94+3492x^95+5852x^96+4890x^97+5880x^98+9154x^99+7872x^100+8268x^101+13332x^102+10188x^103+10956x^104+14134x^105+10224x^106+9642x^107+12736x^108+8052x^109+6774x^110+7782x^111+4590x^112+3738x^113+3574x^114+1728x^115+1134x^116+1030x^117+540x^118+270x^119+166x^120+48x^121+12x^122+20x^123+6x^124+4x^126+6x^129+6x^132+6x^135

The gray image is a linear code over GF(3) with n=156, k=11 and d=87.
This code was found by Heurico 1.16 in 376 seconds.