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

generates a code of length 54 over Z3[X]/(X^2) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+58x^90+174x^93+78x^94+314x^96+438x^97+584x^99+948x^100+734x^102+1806x^103+836x^105+2364x^106+1030x^108+3198x^109+1068x^111+2508x^112+820x^114+1302x^115+432x^117+444x^118+244x^120+36x^121+122x^123+74x^126+44x^129+14x^132+8x^135+4x^138

The gray image is a linear code over GF(3) with n=162, k=9 and d=90.
This code was found by Heurico 1.16 in 5.32 seconds.