The generator matrix

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

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+76x^87+172x^90+192x^93+256x^96+678x^99+1508x^102+1938x^105+1058x^108+194x^111+166x^114+140x^117+98x^120+46x^123+26x^126+6x^129+2x^132+2x^135+2x^144

The gray image is a linear code over GF(3) with n=156, k=8 and d=87.
This code was found by Heurico 1.16 in 0.979 seconds.