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

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+11x^22+14x^24+32x^25+15x^26+32x^27+12x^28+5x^30+5x^32+1x^50

The gray image is a linear code over GF(2) with n=52, k=7 and d=22.
This code was found by Heurico 1.16 in 0.00289 seconds.