What you have planned out there would be fine for a goldfish pond but its not for Koi. Its too small. It also needs to be at least 3 ft. deep and 4 ft. would be even better. What is your winter climate? You have to think about freezing, etc.
Also, the tree is an issue, not only for roots but the leaves that come off in the fall and will go right into your pond. That will make a bunch of extra work for you or you will need to net the pond to keep them out.
I also agree that what you have mapped out is too close to the fence. There is no room there to work, walk around it, landscape, etc.