The generator matrix

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

generates a code of length 55 over Z3[X]/(X^3) who´s minimum homogenous weight is 104.

Homogenous weight enumerator: w(x)=1x^0+336x^104+288x^105+480x^106+750x^107+572x^108+384x^109+894x^110+594x^111+504x^112+792x^113+316x^114+240x^115+294x^116+68x^117+12x^118+6x^119+4x^120+6x^122+14x^123+4x^126+2x^147

The gray image is a linear code over GF(3) with n=495, k=8 and d=312.
This code was found by Heurico 1.16 in 7.1 seconds.