I think that is a good pattern with number #4 shot. Could it be better yes. I use LB #4 for all my field shooting and I use #6 for close in work such as in the woods. I also use the Kicks .665 however I am shooting a Browning BPS. My Benelli Super Black Eagle ii gets used for other bird hunting.
Most on this forum seem to prefer #6 shot in a variety of shells. I have shot the hevi shot and mag blends. Mag blends work okay for me but I prefer LB and hevi shot will not pattern well in my BPS.
If you are not happy with your current pattern or shot size I would suggest experimenting with different size shot and chokes but first read some of the posts on this site. There are some serious Turkey hunters contributing and providing information. These posts will save you time and money.
Welcome to the forum!