The generator matrix

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

generates a code of length 28 over Z2[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+101x^16+74x^18+642x^20+832x^22+2186x^24+2670x^26+3338x^28+2704x^30+2217x^32+806x^34+646x^36+80x^38+70x^40+2x^42+14x^44+1x^48

The gray image is a linear code over GF(2) with n=56, k=14 and d=16.
This code was found by Heurico 1.16 in 6.64 seconds.