The generator matrix

 1  0  0  0  0  0  0  1  1  1  1  0  X  1  0  0  X  1  0  X  1  1  1  1  0  1  0  1
 0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  1  1  1  X  X  1 X+1  X  X  1  1  1  X
 0  0  1  0  0  0  0  0  0 X+1  X  1  1  1  X  1  0 X+1  X  1  X  X X+1 X+1  1  1  X  X
 0  0  0  1  0  0  0  0 X+1  1  X  0 X+1  X  0  1  1  X  1  X  1  0  X  0  0 X+1 X+1  X
 0  0  0  0  1  0  0  0  1  0  1  X X+1  1  1  X  X  X  X X+1  1 X+1  0  1 X+1  1  0  X
 0  0  0  0  0  1  0  1  0  1 X+1  X X+1  1 X+1  0  1  0  0  X X+1  X  0 X+1 X+1  1  1  X
 0  0  0  0  0  0  1  1 X+1  X  X X+1  1 X+1  X  X  0  1  1  0  0  0 X+1  0  0  1  1 X+1
 0  0  0  0  0  0  0  X  X  0  0  X  X  0  X  0  X  0  X  X  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+98x^18+254x^19+455x^20+694x^21+935x^22+1368x^23+1918x^24+2486x^25+2927x^26+3342x^27+3582x^28+3412x^29+3074x^30+2584x^31+1983x^32+1380x^33+940x^34+594x^35+355x^36+214x^37+87x^38+48x^39+26x^40+6x^41+3x^42+2x^43

The gray image is a linear code over GF(2) with n=56, k=15 and d=18.
This code was found by Heurico 1.16 in 36.4 seconds.