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

generates a code of length 53 over Z3[X]/(X^3) who´s minimum homogenous weight is 106.

Homogenous weight enumerator: w(x)=1x^0+54x^106+14x^108+8x^111+2x^114+2x^117

The gray image is a linear code over GF(3) with n=477, k=4 and d=318.
This code was found by Heurico 1.16 in 0.0393 seconds.