The generator matrix

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

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+135x^20+208x^22+191x^24+176x^26+173x^28+88x^30+44x^32+8x^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 1.10 in 0.063 seconds.