This period 16 oscillator is very similar to... I don't know it's name and four eaters. I found syntheses for both objects. I believe that a synthesis could be made for this oscillator. Here's my progress:
It shows the oscillator, steps used and my progress. Of course, the two middle eaters or something similar would have to be made for the top two, but you get what I mean.
The unnamed object at the bottom is a hat. But what seems more striking to me is that the oscillator "frame" looks remarkably like two 14-bit objects, identified by 14.285 on pentadecathlon.com, and identified by 14.172 on Mark Niemec's webpage. I have prepared a synthesis from a couple of components on pentadecathlon.com:
Although components of the stator do seem like they can be synthesized, I believe a complete synthesis would be infeasible at the current time. To synthesize this oscillator, one would need to find a still life configuration that can be 'activated' with a combination of sparks and gliders, such as this partial synthesis of a period-7 oscillator:
x = 15, y = 18, rule = B3/S23
2bobo$3b2o$3bo$10bo$9bo$9b3o4$2b2o$2bo3b2o4b2o$4bo2bo4bobo$6o6bo$o$b2o
b2o3b2o$2bobo4bobo$2bobo6bo$3bo7b2o!
Unfortunately, I can't see a still life that would work for this. If you have a still life in mind, I would suggest using WinLifeSearch to find predecessors of the oscillator.