The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  X  X  1  1  1  1
 0  X  0  0  0  0  0  X  0  0  0  0  X  X  0  X  0  X  X  0  X  0  X  X  0
 0  0  X  0  0  0  0  X  0  0  X  X  X  X  X  0  X  X  X  X  X  0  X  0  X
 0  0  0  X  0  0  0  X  0  X  X  0  0  0  X  X  X  0  X  0  X  0  0  0  X
 0  0  0  0  X  0  0  X  0  X  0  X  0  X  0  0  X  X  X  0  0  X  0  X  0
 0  0  0  0  0  X  0  X  X  0  0  X  0  X  X  X  0  0  X  X  0  X  X  0  X
 0  0  0  0  0  0  X  X  X  0  X  0  0  X  0  X  X  X  0  X  0  0  X  0  0

generates a code of length 25 over Z2[X]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+40x^20+134x^24+55x^28+25x^32+1x^44

The gray image is a linear code over GF(2) with n=50, k=8 and d=20.
This code was found by Heurico 1.16 in 0.015 seconds.