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

generates a code of length 56 over Z3[X]/(X^3) who´s minimum homogenous weight is 111.

Homogenous weight enumerator: w(x)=1x^0+54x^111+162x^112+12x^114+8x^117+6x^129

The gray image is a linear code over GF(3) with n=504, k=5 and d=333.
This code was found by Heurico 1.16 in 0.0519 seconds.