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

generates a code of length 52 over Z3[X]/(X^3) who´s minimum homogenous weight is 105.

Homogenous weight enumerator: w(x)=1x^0+72x^105+8x^108

The gray image is a linear code over GF(3) with n=468, k=4 and d=315.
This code was found by Heurico 1.16 in 0.0366 seconds.