The generator matrix

 1  0  0  0  1  1  1  0  1  1  X  X  1  1  1  1  1  0  1  1  0  X  0  0  1
 0  1  0  0  0  0  0  1 X+1  1  1  1  X  X X+1  1  1  X  0  1  1  1  0  0  X
 0  0  1  0  0  1  1  1  1  X  0 X+1  0  X  1 X+1  X  1  1  1  X  X  1  1 X+1
 0  0  0  1  1  1  0 X+1 X+1  0  1  X  0 X+1  1  X  1  0 X+1  X  0 X+1  1 X+1 X+1
 0  0  0  0  X  0  0  X  X  X  X  0  X  0  X  0  0  X  X  X  0  0  X  0  X
 0  0  0  0  0  X  0  0  0  0  X  0  0  X  X  X  0  X  X  X  X  X  0  0  0
 0  0  0  0  0  0  X  X  0  0  0  X  X  X  0  X  X  0  0  X  X  0  0  X  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+443x^20+777x^24+702x^28+117x^32+7x^36+1x^40

The gray image is a linear code over GF(2) with n=50, k=11 and d=20.
As d=20 is an upper bound for linear (50,11,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 11.
This code was found by Heurico 1.16 in 71.6 seconds.