The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  X  0  0  0  0  X  0  X  X  0  0  X  X  X  X  0  0  0  0  X  X  0  0  X
 0  0  X  0  0  0  X  X  X  0  X  X  X  X  0  0  0  0  0  X  X  0  0  X  X
 0  0  0  X  0  X  0  X  0  X  X  0  X  X  X  0  0  0  X  X  0  0  X  X  X
 0  0  0  0  X  X  0  0  X  X  X  X  X  0  0  X  0  X  X  0  0  0  0  X  X

generates a code of length 25 over Z2[X]/(X^2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+6x^22+9x^24+32x^25+9x^26+6x^28+1x^50

The gray image is a linear code over GF(2) with n=50, k=6 and d=22.
This code was found by Heurico 1.16 in 0.00168 seconds.