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

generates a code of length 52 over Z3[X]/(X^2) who´s minimum homogenous weight is 104.

Homogenous weight enumerator: w(x)=1x^0+54x^104+12x^105+8x^108+4x^111+2x^120

The gray image is a linear code over GF(3) with n=156, k=4 and d=104.
This code was found by Heurico 1.16 in 0.0122 seconds.