The generator matrix

 1  0  0  0  0  1  1  1  1  0  1  0  X  0  1  1  1  X  1  1  1  0  X  X  1  X  X  1
 0  1  0  0  0  0  0  0  0  0  0  0  0  0  X  X X+1  1  1  1 X+1  1  X  X  1  X  1 X+1
 0  0  1  0  0  0  1  0  1  1  X  1  1  X  1 X+1  1 X+1 X+1  1  X  X  X  1  1  1  0  1
 0  0  0  1  0  0  1  1  0 X+1  1  X  1  1  1  X  0  1  0  1  1  X  X  0 X+1  X  1 X+1
 0  0  0  0  1  1  0  1 X+1 X+1  0  1  X  1  1  0 X+1  1  X X+1  0  1  1  X  0  1  X  0
 0  0  0  0  0  X  0  0  0  0  X  X  X  X  X  X  0  X  X  X  X  0  X  X  0  0  0  X
 0  0  0  0  0  0  X  0  X  X  0  0  X  X  X  X  0  X  0  X  0  X  X  X  0  0  X  X
 0  0  0  0  0  0  0  X  X  0  X  0  X  X  0  X  X  0  0  X  0  X  0  0  0  0  X  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+217x^20+574x^22+1054x^24+1342x^26+1725x^28+1456x^30+1163x^32+432x^34+183x^36+34x^38+6x^40+2x^42+3x^44

The gray image is a linear code over GF(2) with n=56, k=13 and d=20.
This code was found by Heurico 1.16 in 5.27 seconds.