The generator matrix

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

generates a code of length 54 over Z3[X]/(X^2) who´s minimum homogenous weight is 91.

Homogenous weight enumerator: w(x)=1x^0+240x^91+378x^92+696x^93+1038x^94+1686x^95+1826x^96+2322x^97+3654x^98+3996x^99+4086x^100+6312x^101+6854x^102+7068x^103+9750x^104+9504x^105+9000x^106+11748x^107+11630x^108+9936x^109+12894x^110+11044x^111+9138x^112+10356x^113+7950x^114+5652x^115+5784x^116+3706x^117+2892x^118+2448x^119+1418x^120+900x^121+510x^122+316x^123+198x^124+90x^125+76x^126+18x^127+18x^129+6x^132+4x^135+4x^138

The gray image is a linear code over GF(3) with n=162, k=11 and d=91.
This code was found by Heurico 1.16 in 397 seconds.