The generator matrix

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

generates a code of length 54 over Z3[X]/(X^3) who´s minimum homogenous weight is 98.

Homogenous weight enumerator: w(x)=1x^0+402x^98+784x^99+1932x^100+4002x^101+4656x^102+6978x^103+10272x^104+11582x^105+15078x^106+20388x^107+18860x^108+19278x^109+21090x^110+14870x^111+11538x^112+8352x^113+3478x^114+1884x^115+918x^116+344x^117+138x^118+126x^119+76x^120+24x^121+60x^122+24x^123+12x^124

The gray image is a linear code over GF(3) with n=486, k=11 and d=294.
This code was found by Heurico 1.16 in 52.1 seconds.