The generator matrix

 1  0  0  0  0  0  0  1  1  1  0  1  X  1  1  1  X  X  0  1  X  X  0  1  0  1  1  1
 0  1  0  0  0  0  0  X X+1  X  1 X+1  X  0  X  1  1  1  0  X  1  1  1  1  0 X+1  0  0
 0  0  1  0  0  0  0  0  1 X+1  X X+1  1 X+1  X  1 X+1  X  0  X X+1  X  1  1  1 X+1  1  0
 0  0  0  1  0  0  0  0  0  0  0  0  X X+1  1  1  1 X+1  X X+1  X X+1  X  0 X+1 X+1  0  0
 0  0  0  0  1  0  0  1  0 X+1  X  0  1  X  0  1  1  1  1  X  X X+1 X+1  1  X  X  1  0
 0  0  0  0  0  1  0  1  X  X  1 X+1  1 X+1  1 X+1  1 X+1  X  0  X  1  1  0  X  X  0  0
 0  0  0  0  0  0  1  1 X+1  0  1  X X+1 X+1  X X+1  0  0 X+1  X X+1  1  1  0  1  0  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+94x^18+90x^19+284x^20+340x^21+569x^22+724x^23+979x^24+1178x^25+1393x^26+1652x^27+1496x^28+1816x^29+1426x^30+1352x^31+1081x^32+692x^33+528x^34+258x^35+228x^36+68x^37+85x^38+20x^39+27x^40+2x^41+1x^42

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 17.9 seconds.