The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  X  X  0  1  X  1  X  1  X  1  1  1  X  1  0  1  1
 0  1  0  0  0  0  0  0  0 X+1  1  1  X  1  1  1  1  1  X  1  0  1  0  X  0  X X+1  0
 0  0  1  0  0  0  1  1  1  1  1  X  0 X+1  0  1  X  X X+1  X X+1 X+1  0  1  1  1  0  0
 0  0  0  1  0  1  1  0  1  0  X X+1  1  0 X+1  X  0  0 X+1  1  1  1  1 X+1  0  1  0  0
 0  0  0  0  1  1  0  1  1 X+1  X  0 X+1  0  1  1  0 X+1 X+1  1  X  0  0  0  X  1  0  0
 0  0  0  0  0  X  0  0  0  X  0  0  X  X  0  X  0  X  0  X  X  X  0  0  X  0  X  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  X  0
 0  0  0  0  0  0  0  X  0  0  X  X  X  X  0  0  0  0  X  X  X  0  X  0  0  X  0  0
 0  0  0  0  0  0  0  0  X  0  X  X  X  X  X  X  X  X  X  0  X  X  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+79x^18+88x^19+308x^20+320x^21+580x^22+724x^23+930x^24+1212x^25+1395x^26+1716x^27+1576x^28+1756x^29+1392x^30+1292x^31+1031x^32+724x^33+565x^34+260x^35+228x^36+84x^37+76x^38+16x^39+22x^40+9x^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 16 seconds.