The generator matrix

 1  0  0  0  0  1  1  1  1  0  X  1  1  1  0  0  1  X  X  0  X  X  1  1  1
 0  1  0  0  0  X  X  1  1  1  1 X+1  X  0  1  1  0  0  1  0  1  1  0  X X+1
 0  0  1  0  0  0  0  0  X  X  0 X+1  1 X+1  1  1  1  1  X  1  X  0  1  X  0
 0  0  0  1  0  0 X+1  X X+1  X X+1  X  1  1  0 X+1  X  X  1  X X+1  X  1  X  0
 0  0  0  0  1  1 X+1  1  0  1  1  X  0 X+1  X X+1  0  1  X  X X+1  0  0  X  X

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+141x^20+200x^22+191x^24+170x^26+179x^28+100x^30+32x^32+10x^34

The gray image is a linear code over GF(2) with n=50, k=10 and d=20.
As d=20 is an upper bound for linear (50,10,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 10.
This code was found by Heurico 1.16 in 0.0423 seconds.