How to plot a matrix in a checkerboard style

I am trying to make my matrix Im look like the image below. I have tried playing around with the grid size, but to no avail...

Im = [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
      0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
      0 0 1 0 0 0 1 1 0 0 0 0 0 0 0;
      0 1 0 0 0 0 1 0 0 0 0 1 0 0 0;
      0 1 0 1 1 0 1 0 0 0 0 1 1 1 0;
      0 0 0 1 1 0 1 0 0 0 0 1 0 0 0;
      0 0 1 0 1 0 1 1 0 0 0 0 0 0 0;
      0 0 0 1 1 0 1 1 0 0 0 0 0 0 0;
      0 0 0 0 0 0 0 1 0 0 0 0 0 1 0;
      0 0 0 0 0 0 0 0 0 0 0 0 1 0 0;
      0 0 0 1 0 0 0 1 0 0 0 1 1 0 0;
      0 0 1 1 0 0 1 1 0 0 0 1 0 0 0;
      0 0 0 1 0 0 1 1 0 0 0 1 1 0 0;
      0 0 0 0 0 0 0 0 0 0 1 0 0 0 0;
      0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
     ];

figure
imagesc(Im)
grid on
set(gca,'xtick',[0:1:length(Im)])
set(gca,'ytick',[0:1:length(Im)])

Answer 1

[DGM]

Something like this should be a start:

Im = [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
    0 0 1 0 0 0 1 1 0 0 0 0 0 0 0;
    0 1 0 0 0 0 1 0 0 0 0 1 0 0 0;
    0 1 0 1 1 0 1 0 0 0 0 1 1 1 0;
    0 0 0 1 1 0 1 0 0 0 0 1 0 0 0;
    0 0 1 0 1 0 1 1 0 0 0 0 0 0 0;
    0 0 0 1 1 0 1 1 0 0 0 0 0 0 0;
    0 0 0 0 0 0 0 1 0 0 0 0 0 1 0;
    0 0 0 0 0 0 0 0 0 0 0 0 1 0 0;
    0 0 0 1 0 0 0 1 0 0 0 1 1 0 0;
    0 0 1 1 0 0 1 1 0 0 0 1 0 0 0;
    0 0 0 1 0 0 1 1 0 0 0 1 1 0 0;
    0 0 0 0 0 0 0 0 0 0 1 0 0 0 0;
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
    ];

hp = pcolor(padarray(Im,[1 1],'replicate','post'));
hp.EdgeColor = [1 0 0];
hp.LineWidth = 2;
colormap(gray(2))
set(gca,'ydir','reverse')
axis equal