Hi Conrad:
Your pond is about the same size as my pond. My husband built a gravity fed filtration system and I do not know anything about the engineering of that. I just know we have a bottom drain and the waste goes into the filter by itself and settles in the bottom of filter before it gets pumped back out as clean water into the pond.
It has four chambers that forces the water flow to go over one chamber and under another then over and under, four chambers all together, with filter matts and larva rocks and bio balls so by the time it gets pumped back in the bad stuff has been settled.
It is 4 foot wide, 8 foot long and 4 foot deep. But the good news is I only have to clean it twice a year.
We have three water falls for oxigenation. One water fall has a seperate pump and the other two waterfalls are how the clean water gets back to the pond.
He found directions on the interenet. Alas, he is done and no longer has anything to do with it, unless a problem occurs.
So, YES, you need filteration and aireation. These fish get to 3 feet sometimes.