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

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+218x^102+54x^104+414x^105+324x^107+984x^108+2106x^110+1396x^111+432x^113+262x^114+188x^117+112x^120+62x^123+4x^126+2x^138+2x^153

The gray image is a linear code over GF(3) with n=495, k=8 and d=306.
This code was found by Heurico 1.16 in 0.275 seconds.