The generator matrix

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

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+240x^98+354x^99+432x^100+1200x^101+1594x^102+2448x^103+3342x^104+3080x^105+6138x^106+7062x^107+4900x^108+8100x^109+7248x^110+3876x^111+4464x^112+2148x^113+1198x^114+288x^115+372x^116+202x^117+210x^119+68x^120+36x^122+22x^123+12x^125+4x^126+4x^129+2x^132+2x^135+2x^138

The gray image is a linear code over GF(3) with n=486, k=10 and d=294.
This code was found by Heurico 1.16 in 7.78 seconds.