The problem with this backyard, besides its small... is that it has really really good drainage, so I might need to water the corn well.
I also know you shouldn’t plant corn and tomatoes near each other but that squash and beans work well with corn.
So in an area of about 4ft by 12ft you could have 36 corn plants,and some good corn plants like "incredible" will produce two ears per plant in a good growing season with proper fertilizer.That's up to 72 ears of corn.
Corn loves nitrogen so when it start growing about 5-6 inches tall throw some around the plants then when it starts "tassel ling" do it again.
Well drained soil works fine My garden is well "drained". Actually a well drained garden does the best.