The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  1  1  0  1  1  1  1  0  1  0  0  0  1  1  1
 0  1  1  0  1  1  0  1  1  0  1  1  0  X X+1  1  0 X+1 X+1  0  1 X+1  1  1  1  0  0  0
 0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  X  0  X  X  0  X  X  X  X  X  0  0  0
 0  0  0  X  0  0  0  0  0  0  0  0  0  X  0  X  X  X  0  0  0  X  X  0  X  X  0  0
 0  0  0  0  X  0  0  0  0  0  0  0  0  0  X  0  X  0  X  0  X  X  X  0  X  X  0  0
 0  0  0  0  0  X  0  0  0  0  0  0  0  0  X  0  0  X  0  X  0  X  X  X  0  X  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  0  X  X  X  X  0  X  0  X  X  0  0
 0  0  0  0  0  0  0  X  0  0  0  0  0  0  X  X  X  X  0  X  X  0  X  0  0  0  0  0
 0  0  0  0  0  0  0  0  X  0  0  0  X  X  X  X  X  X  X  X  X  X  0  0  X  0  0  0
 0  0  0  0  0  0  0  0  0  X  0  0  X  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X
 0  0  0  0  0  0  0  0  0  0  X  0  X  X  X  0  X  X  X  0  0  0  X  0  0  X  X  X
 0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  0  X  X  0  X  X  X  X  X  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+108x^16+160x^18+96x^19+180x^20+64x^21+368x^22+928x^23+928x^24+992x^25+1488x^26+2016x^27+1700x^28+2016x^29+1568x^30+992x^31+825x^32+928x^33+384x^34+64x^35+284x^36+96x^37+112x^38+56x^40+16x^42+12x^44+2x^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 6.67 seconds.