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

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+100x^87+260x^90+362x^93+452x^96+54x^98+532x^99+540x^101+574x^102+2160x^104+638x^105+4320x^107+652x^108+4320x^110+682x^111+1728x^113+660x^114+578x^117+420x^120+272x^123+204x^126+120x^129+38x^132+14x^135+2x^147

The gray image is a linear code over GF(3) with n=162, k=9 and d=87.
This code was found by Heurico 1.16 in 9.1 seconds.