I tried doing a search for this one, but the only topic I could find was actually for level 18.
This is the first map I've really had trouble on so far, and I can't a strategy for it.
I've tried expanding to good worlds to build an army to defend the greys with. Didn't work because by the time I had an army, they attacked their first sphere and were decimated so heavily that they were destroyed the next time they moved or when another color sent an expeditionary force.
I've tried rapid expansion to the north to find affiliated seedlings and more greys. I found small pockets of both, but it wasn't enough to stop the same losing conditions as the previous strategy.
The last thing I tried, and I really thought it would work, is aggressively assault both the worlds the large grey pocket moves to, and clear out all the worlds closest to it to prevent enemy retaliation against grey. This worked well, but my forces were so drained that when grey started moving, it took all of my best worlds and I was left with just a smattering of poor worlds, and then either I would be conquered by the other colors, or the other colors would slip in the back door and conquer all the worlds that grey took over and kill them off.