56 pushups in 30 seconds? It seems to me the only way to do that is to either a) do them with extremely bad form, b) not go down completely, c) both of those. People like eshlow (author of "Overcoming Gravity") at /r/bodyweightfitness recommend a tempo of 10x1: lowering yourself for one second, staying 0 seconds at the bottom, pushing up as hard and fast as possible (x = explode), and holding for one second at the top. Using this tempo, you can do a max of 15 per 30 seconds.
Yes, it's a different form than you described. I go all the way down and basically go extremely quickly up and down without slowing down the fall phase. My muscles are explosive, I am a good natural fit for tennis, squash, basketball, ice hockey, alpine skiing, sprints, etc. not for endurance (this needs a lot of work). Moreover, I have a very good skeletal maneuverability that doesn't inhibit my movements as is the case with many other muscular people. Also, it took me ~6 months to get to this level. YMMV
