The generator matrix

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

generates a code of length 55 over Z3[X]/(X^3) who´s minimum homogenous weight is 102.

Homogenous weight enumerator: w(x)=1x^0+536x^102+702x^103+1944x^104+3686x^105+3042x^106+4584x^107+6744x^108+3930x^109+6630x^110+8088x^111+4140x^112+5202x^113+4696x^114+1878x^115+1464x^116+1170x^117+372x^118+78x^119+68x^120+18x^121+18x^122+24x^123+12x^124+14x^126+6x^128+2x^129

The gray image is a linear code over GF(3) with n=495, k=10 and d=306.
This code was found by Heurico 1.16 in 6.15 seconds.