Yes, it is possible to do that kind of extraction. People do cold water extractions with good results, even though that's not a pure extraction and it will still make you sick. Keep in mind that the nausea comes from motion sickness and you really can't avoid it even with the best of extractions. If you are looking for caps, you can find DXM caps all over the internet (DXM HBr). There is also pure DXM powder available (Don't know the quality of it though), you could put those in capsules as well.
But yes, you can do an extraction on your own as well from the syrup, it would require lab grade chemicals and equipment should you wish to do it safely