The generator matrix

 1  0  0  0  0  0  0  0  1  1  1  1  1  0  1  1  0  X  X  1  X  0  X  1  1  1  1  1
 0  1  0  0  0  0  0  0  0  X  0  X  0  X  0  1  1  1  1  1  X  1  1  1  0 X+1  X  0
 0  0  1  0  0  0  0  0  0  X  1  1  0  1  X  0 X+1  1  X X+1  1  1  X  0  0  0  X  0
 0  0  0  1  0  0  0  0  1  0  0  1 X+1  1 X+1  X X+1  0  X  0 X+1 X+1 X+1  X  1  0  0  0
 0  0  0  0  1  0  0  0  1  0 X+1  0  1 X+1  X X+1 X+1  1 X+1  X  1  1 X+1  X X+1  0 X+1  0
 0  0  0  0  0  1  0  0  1  1  1  0  X X+1  1  X  X  1 X+1  1 X+1  1  0  X  X X+1  1  0
 0  0  0  0  0  0  1  0  1  1  X X+1 X+1  1  0  X  0 X+1  X  1  X  1 X+1  0  0  X  0  X
 0  0  0  0  0  0  0  1  X  1 X+1  X  1 X+1  1  X X+1  X  1  0 X+1 X+1  0  X  1  1  X X+1

generates a code of length 28 over Z2[X]/(X^2) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+72x^17+241x^18+448x^19+837x^20+1224x^21+1888x^22+2786x^23+3812x^24+5144x^25+5988x^26+6792x^27+7050x^28+6680x^29+6152x^30+5036x^31+3915x^32+2832x^33+1937x^34+1224x^35+729x^36+416x^37+176x^38+98x^39+40x^40+16x^41+2x^42

The gray image is a linear code over GF(2) with n=56, k=16 and d=17.
This code was found by Heurico 1.11 in 56 seconds.