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

generates a code of length 56 over Z3[X]/(X^3) who´s minimum homogenous weight is 109.

Homogenous weight enumerator: w(x)=1x^0+96x^109+240x^110+8x^111+78x^112+108x^113+8x^114+96x^115+72x^116+2x^117+12x^119+4x^120+2x^123+2x^132

The gray image is a linear code over GF(3) with n=504, k=6 and d=327.
This code was found by Heurico 1.16 in 0.0695 seconds.