The generator matrix

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

generates a code of length 26 over Z2[X]/(X^2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+44x^22+67x^24+45x^26+54x^28+35x^30+4x^32+3x^34+1x^36+1x^38+1x^44

The gray image is a linear code over GF(2) with n=52, k=8 and d=22.
This code was found by Heurico 1.16 in 0.00842 seconds.