The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  1  X  X  0  0  1  X  1  1  0  1  1  X
 0  1  0  1  0  1  1  0  X  1  1  X  0  1  1  0  X  X  1  0 X+1  1  1 X+1  1
 0  0  1  1  1  0  1  X  1  0 X+1  1  0  0  1  1  1  1  1 X+1  0 X+1 X+1 X+1  X
 0  0  0  X  0  0  0  X  X  X  X  0  0  X  0  0  X  0  0  X  0  X  0  X  0
 0  0  0  0  X  0  0  0  X  0  X  X  X  X  0  0  X  0  X  X  X  0  X  0  X
 0  0  0  0  0  X  0  0  0  X  0  0  0  0  X  X  X  X  0  X  0  X  X  X  0
 0  0  0  0  0  0  X  X  X  X  X  X  X  0  X  0  0  0  X  X  0  X  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+143x^20+182x^22+208x^24+186x^26+174x^28+74x^30+47x^32+6x^34+3x^36

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 0.175 seconds.