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

generates a code of length 56 over Z3[X]/(X^3) who´s minimum homogenous weight is 112.

Homogenous weight enumerator: w(x)=1x^0+54x^112+14x^114+8x^117+2x^120+2x^126

The gray image is a linear code over GF(3) with n=504, k=4 and d=336.
This code was found by Heurico 1.16 in 0.0495 seconds.