The generator matrix

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

generates a code of length 54 over Z3[X]/(X^3) who´s minimum homogenous weight is 101.

Homogenous weight enumerator: w(x)=1x^0+204x^101+198x^102+564x^104+460x^105+648x^106+282x^107+1398x^108+1296x^109+528x^110+490x^111+150x^113+50x^114+96x^116+32x^117+96x^119+30x^120+24x^122+12x^123+2x^147

The gray image is a linear code over GF(3) with n=486, k=8 and d=303.
This code was found by Heurico 1.16 in 0.287 seconds.