The generator matrix

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

generates a code of length 26 over Z2[X]/(X^2) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+14x^21+37x^22+45x^24+70x^25+42x^29+22x^30+17x^32+2x^33+5x^38+1x^40

The gray image is a linear code over GF(2) with n=52, k=8 and d=21.
This code was found by Heurico 1.16 in 3.38 seconds.