If your pond is 10' by 16' by 4 feet deep. I think you might need about 4 times as much greenhouse to have as much grow bed as you might be able to support. However 100 Koi, I would say you probably need at least 100-400 cubic feet of grow bed depending on the size of the koi and how much you will be feeding them.
You can always go deeper (like double) than typical on the GB/GB's to maximize media. I would look at additional filtration to maintain a healthy system. Lots out there on pond filtration, large and small. My pond is a bit smaller than what you are talking, but I have a brush filter, ahead of a barrel-style bio filter. Both were DIY. They work great and there are no GB's connected to this pond. I'd also look at the moving bed type filters. They get great reviews.