Plot Checkboard Pattern with meshgrid?

Hi, I'm new to matlab and my prof asked us to plot an image like the following:

We are supposed to used the mesh grid function and modulate it with sin and cos as well as change the contrast to 20%. There's also some specifications for the period of the design. I've come up with the following code but it results in a different image thats more like this : Not sure how to create the one he is asking for. Thanks in advance for your help.

[X,Y] = meshgrid(1:40,1:40)
Z = sin(0.5*pi*Y).*cos(0.5*pi*X)
contour(X,Y,Z,20)
colormap(gray)

[KALYAN ACHARJYA]

Ok @Raymond Got it

[Geoff Hayes]

Raymond - try increasing the number of coordinates used in the meshgrid.

coords = linspace(1,40,500);
[X,Y] = meshgrid(coords, coords);

Experiment with other values to see the change to the checkerboard.