The generator matrix

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

generates a code of length 28 over Z2[X]/(X^2) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+57x^18+98x^19+247x^20+284x^21+529x^22+738x^23+915x^24+1256x^25+1442x^26+1724x^27+1731x^28+1696x^29+1522x^30+1260x^31+1006x^32+792x^33+477x^34+258x^35+181x^36+68x^37+61x^38+18x^39+13x^40+8x^42+1x^44+1x^48

The gray image is a linear code over GF(2) with n=56, k=14 and d=18.
This code was found by Heurico 1.16 in 14.9 seconds.