The generator matrix

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

generates a code of length 28 over Z2[X]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+76x^20+80x^22+333x^24+304x^26+477x^28+304x^30+309x^32+80x^34+70x^36+13x^40+1x^44

The gray image is a linear code over GF(2) with n=56, k=11 and d=20.
This code was found by Heurico 1.16 in 0.183 seconds.