Well, have you ever seen the little table top minature gardens? That's the sort of thing you're probably looking at. Lots of minature evergreens, mosses, dianthus, etc.

What are you planning to grow ... flowers, herbs, vegetables?

You might want to take a look at the "Square Foot Gardening" forum. You might be surprised at how much you can grow in a 4x4 square. Faced with a small area, people often grow up, rather than out (training plants onto poles, trellises, etc.) and make succession plantings (a summer veggie or flowering plant replaces a spent spring crop like spinach, peas or lettuce, which is then replaced by a late crop like spinach, chard or broccoli). Radishes mature quickly and take up little space. I plant my garlic in October/November then harvest in May, so they make use of a bed when it would otherwise lie empty. When gardening so intensively, though, it is even more important to prepare the soil well and provide sufficient fertilizer of the type that you choose.

There are also varieties of vegetables and fruits developed especially for container gardening so are smaller and might work well in your small plot.

Good luck & enjoy!

Is his a plot just for the growing season? I guess that would limit you to just annuals!

If you have a place that can be heated, why not try a terrarium? In this you could grow a variety of miniature plants. My special recommendation would be orchids.