The generator matrix

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

generates a code of length 55 over Z3[X]/(X^2) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+118x^96+60x^97+120x^98+590x^99+306x^100+402x^101+1056x^102+504x^103+486x^104+1444x^105+570x^106+648x^107+1904x^108+810x^109+882x^110+1986x^111+870x^112+858x^113+1644x^114+696x^115+570x^116+1382x^117+378x^118+336x^119+518x^120+132x^121+60x^122+202x^123+24x^124+12x^125+50x^126+18x^127+20x^129+6x^130+10x^132+4x^135+2x^138+2x^141+2x^144

The gray image is a linear code over GF(3) with n=165, k=9 and d=96.
This code was found by Heurico 1.16 in 4.81 seconds.