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  1  1  1  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 2X^2+2X X^2 X^2+X X^2+2X X^2+X X^2+2X X^2+2X X^2+X X^2 X^2  0 2X^2+X X^2 2X^2+2X 2X X^2+X  X X^2+X X^2+2X X^2+2X X^2 2X  X 2X X^2  X  0 2X^2 2X^2  0
 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 2X^2  0 2X^2 2X^2 2X^2 2X^2 X^2 X^2 X^2 2X^2 2X^2 X^2 2X^2  0 2X^2 2X^2 X^2 X^2  0  0 X^2  0  0  0 X^2 2X^2 2X^2  0  0
 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 X^2 X^2 X^2 X^2 X^2  0 2X^2 2X^2 X^2 X^2 2X^2 2X^2 2X^2 2X^2 X^2 X^2 X^2  0  0 2X^2  0  0  0 2X^2 2X^2 X^2 2X^2 X^2  0 X^2
 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 X^2  0 X^2  0 X^2 X^2 X^2 2X^2 2X^2 X^2  0 X^2 2X^2 X^2 X^2 X^2 2X^2 X^2  0 2X^2  0  0 X^2 2X^2 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+444x^105+366x^108+306x^111+4374x^112+720x^114+108x^117+18x^120+126x^123+90x^126+6x^132+2x^162

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 86.8 seconds.