The generator matrix

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

generates a code of length 25 over Z2[X]/(X^2) who�s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+108x^24+19x^32

The gray image is a linear code over GF(2) with n=50, k=7 and d=24.
As d=24 is an upper bound for linear (50,7,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 7.
This code was found by Heurico 1.16 in 1.12 seconds.