That looks like a printed bottom-loaded antenna. I'm no expert, but I think a full-length 1/2-wave vertical dipole antenna might improve things if you want an omni-directional response, or a Yagi array if you want a directional response.
Thanks Alec.
That would be more than I require so I'll try relocating the base unit.
I was hoping I could add a small coil or something similar just to make it a tad more effective.
This is an arduino where I did something like this, this is a wifi device, so I was fortunate in that there is plenty of antenna's around for wifi frequencies, I just pinched one off an old router that already had a connector on the end.
I pulled the ant off the board and soldered on a socket, range is now 3x.
If your device is wifi you can do this, or you could build your own ant, but it can get tricky.
I would imagine it's intended for simple garage door remotes, so simply receives the small data packet and then retransmits it - it's probably fairly dependent on what's been transmitted.