The generator matrix

 1  0  0  0  0  0  1  1  1  X  1  1  0  X  1  X  1  1  X  1  1  1  0  1  1  1  1  1
 0  1  0  0  0  0  0  0  0  1  1 X+1  0  X  X  1 X+1  1  X X+1 X+1  1  1  X  X  X X+1 X+1
 0  0  1  0  0  0  0  0  0  0  1 X+1  1  1  1 X+1  1  1  0  X  0  X X+1  1  0  1  X  1
 0  0  0  1  0  0  0  1  1  1  0 X+1 X+1  0  X  X X+1 X+1  1  1  0  1  1  0  X  1  1  1
 0  0  0  0  1  0  1  1  0  1  0  1  X  1 X+1 X+1  0 X+1  1  0  1  0  1  X  0  0  X  X
 0  0  0  0  0  1  1  0  1  1  X X+1  X X+1 X+1  X  0  0  1 X+1  0  0 X+1  X  1 X+1  0  X
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  X  0  0  0  X
 0  0  0  0  0  0  0  X  0  0  X  0  X  X  X  X  X  0  0  0  X  X  0  X  X  X  0  0
 0  0  0  0  0  0  0  0  X  0  0  X  X  X  0  X  X  0  X  X  0  X  0  0  X  X  0  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+115x^18+206x^19+474x^20+658x^21+1081x^22+1282x^23+1912x^24+2502x^25+2832x^26+3464x^27+3390x^28+3648x^29+3058x^30+2448x^31+1987x^32+1448x^33+979x^34+506x^35+406x^36+190x^37+117x^38+30x^39+20x^40+2x^41+10x^42+2x^44

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 45.8 seconds.