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

generates a code of length 56 over Z3[X]/(X^3) who´s minimum homogenous weight is 105.

Homogenous weight enumerator: w(x)=1x^0+192x^105+174x^106+186x^107+496x^108+324x^109+618x^110+880x^111+948x^112+918x^113+784x^114+390x^115+150x^116+114x^117+54x^118+42x^119+92x^120+42x^121+18x^122+66x^123+12x^124+6x^125+46x^126+6x^128+2x^150

The gray image is a linear code over GF(3) with n=504, k=8 and d=315.
This code was found by Heurico 1.16 in 0.261 seconds.