The generator matrix

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

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+43x^18+26x^19+124x^20+140x^21+295x^22+330x^23+457x^24+608x^25+691x^26+932x^27+872x^28+952x^29+683x^30+628x^31+490x^32+320x^33+289x^34+130x^35+92x^36+28x^37+45x^38+2x^39+11x^40+1x^42+1x^46+1x^48

The gray image is a linear code over GF(2) with n=56, k=13 and d=18.
This code was found by Heurico 1.16 in 2.23 seconds.