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.