It would take a bit of work to make your entire hutch look like barn wood. Here is tutorial that explains the colors in the process but it is done on a flat table top like surface. https://www.thehouseofsmiths.com/2012/04/faux-barn-wood-painting-tutorial.html?m=1
I painted my hutch with Annie Sloan chalk paint in charcoal gray. Rustoleum Chalk in charcoal is almost exactly the same color and a bit less expensive. Perhaps you could make the back of your hutch behind the glass and the shelves look like barn wood to compliment what color you choose to paint your hutch rather than try to make the entire hutch look like barn wood.
Here's a Hometalk idea to make your hutch look like weather wood. Maybe this would work too!
Sharon: mabe this will help (...and you need get rid of scrolling on glass and change hardware to rustic)
Leave it outside to weather naturally, or rub it down with a fine sandpaper. Use a pale silver type grey emulsion to dry brush on all over, letting some of the old finish as you go. Let it dry then rub some of it back. repeat using the colours you want in your barnwood look. Stop when you feel you have achieved the look . Leave as is or seal with either clear or antique wax. Hope that helps.
I think your easiest method would really be to chalk paint it gray and add actual weathered barn wood to the back. Take the glass out and also replace the shelves. Trying to "make" it look like barn wood is likely to look cheesy imho.
Check that pin ...instructions are so easy https://www.pinterest.com/pin/605734218610774832/
The easiest way to get a Barn look.......Take it to the barn and let it sit for a few years. It will age very fast and you'll see just how strong its bones are.......lol.