The generator matrix

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

generates a code of length 52 over Z2[X]/(X^3) who�s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+3x^52+16x^53+3x^54+8x^55+1x^58

The gray image is a linear code over GF(2) with n=208, k=5 and d=104.
This code was found by Heurico 1.16 in 0.0673 seconds.