The generator matrix

 1  0  0  0  0  0  1  1  1  X  1  1  0  0  X  1  1  X  X  X  0  X  X  0  1  1  X  1
 0  1  0  0  0  0  0  0  0  1  1  1  X  X  1 X+1  1  0  1  1  X  X  X  0  0 X+1  0  0
 0  0  1  0  0  0  0  0 X+1  0  1 X+1  1  1  X  0  X  1 X+1 X+1  0  1  1  0 X+1  X  1  0
 0  0  0  1  0  0  0  1  1  1  0 X+1 X+1 X+1  0  1  X  0  1  X  1  1 X+1  1  0  1  0  0
 0  0  0  0  1  0  1  1  0  1  0  1  0  X X+1  1  X  1  X  0  X  1 X+1 X+1 X+1  0  0  0
 0  0  0  0  0  1  1  0 X+1  1  X X+1 X+1  0  0  0 X+1 X+1  1  0  1  X  1  0 X+1  X X+1  0
 0  0  0  0  0  0  X  0  X  0  0  X  0  X  0  X  0  X  0  0  X  0  X  X  X  X  X  0
 0  0  0  0  0  0  0  X  0  0  X  0  0  X  X  X  0  0  X  0  0  X  X  X  X  X  X  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+46x^18+162x^19+220x^20+368x^21+577x^22+720x^23+983x^24+1254x^25+1385x^26+1532x^27+1697x^28+1602x^29+1518x^30+1358x^31+973x^32+750x^33+516x^34+296x^35+210x^36+118x^37+49x^38+26x^39+11x^40+4x^41+5x^42+2x^43+1x^44

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 18 seconds.