The generator matrix

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

generates a code of length 28 over Z2[X]/(X^2) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+18x^26+28x^28+12x^30+3x^32+2x^42

The gray image is a linear code over GF(2) with n=56, k=6 and d=26.
This code was found by Heurico 1.16 in 0.181 seconds.