The minute you said 4 foot square I thought square foot garden. You can grow up to 12 bean plants in a square foot. About the same number of lettuces in a square foot. Lots of green onions can be grown in a square foot, and if you plant a 1 bush, cherry or grape tomato in (the latter 2 trained up^) you have salad.
Veggies like sun more than shade and need a 6 good hours of sunlight at least. If your soil is moist all the time make sure its not mucky. No veggie thrives in muck and you would want to lighten up the soil with some pine bark fines (very small pine bark, not huge chunks, sometimes sold as a soil amendment), course sand, chopped up oak leaves, perlite etc. Organic matter that creates a lighter and airy atmosphere for good healthy roots.
Better yet! You have 16 square feet. I wasn't thinking was I?...Ha!
1 eggplant can grow in 2 of those square feet and you can plant eggplants 2 feet apart so you could have more then 1! Some plant eggplants closer, but mine tend to bush out a lot and I like to do 2 feet between them so they can be comfortable...