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

generates a code of length 26 over Z2[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+15x^24+32x^26+15x^28+1x^52

The gray image is a linear code over GF(2) with n=52, k=6 and d=24.
This code was found by Heurico 1.16 in 0.00292 seconds.