The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  1  0  1  1  0  X  1  1  1  1  X  1  1  1  1
 0  1  1  0  1  1  0  1  1  0  1  1  0 X+1  1 X+1  0  1  X X+1 X+1 X+1  1  0  0  0  0  0
 0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  0  0  0  0  0
 0  0  0  X  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  X  0  0  0  0  0  0  0
 0  0  0  0  X  0  0  0  0  0  0  0  X  X  X  0  0  0  X  X  X  X  0  0  0  0  0  0
 0  0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  0  X  X  X  0  0  X  0  0  0  0  0
 0  0  0  0  0  0  X  0  0  0  0  X  0  0  X  X  0  X  X  0  X  X  0  0  0  0  0  0
 0  0  0  0  0  0  0  X  0  0  0  X  X  0  0  X  X  X  0  0  X  0  X  0  0  0  0  0
 0  0  0  0  0  0  0  0  X  0  0  X  X  0  X  0  X  X  0  X  0  X  0  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  X  0  X  0  X  X  0  X  0  0  0  X  X  X  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  0  X  0  X  X  0  X  X  0  0  X  0  X  X  0  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+330x^16+192x^18+22x^20+640x^22+1346x^24+224x^26+2044x^28+480x^30+2081x^32+480x^34+142x^36+32x^38+178x^40

The gray image is a linear code over GF(2) with n=56, k=13 and d=16.
This code was found by Heurico 1.16 in 1.89 seconds.