Most tourists don’t know, that codeine is prohibited all over the country. Respectively, bringing into UAE medicines, containing codeine, may be the reason for a big fine or even imprisonment.
Alongside, it is also prohibited to bring some sedative and drug-containing medicines. If you need to take with you some prescription, you should have it translated in advance before the trip. Drug-containing medicines can be brought only with a special permission, which should be taken in advance. Codeine is for example in "Pentalgin" and "Sedalgin" which are quite popular worldwide.
Check up on the customs is optional, but it is done more and more often recently.