The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  1  1  X  X  1  1  X  X X^2  X  X  1  1  X X^2  X  X X^3 X^2  0 X^2  X X^2  X X^3 X^2  X  X  X
 0 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3  0  0  0 X^3  0

generates a code of length 51 over Z2[X]/(X^4) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+25x^52+4x^54+2x^58

The gray image is a linear code over GF(2) with n=408, k=5 and d=208.
This code was found by Heurico 1.16 in 0.062 seconds.