tap water is full of e coli. streppticcuos, and everything in between and that bacteria will multiply. the colder the temperature the slower the rate of bacterial growth. So I agree I would not keep it longer than a week and that is if it kept in the fridge.
As for the ice cubes I am uncertain how the codeine would stand up to being frozen. I always avoid letting my CWE freeze for fear of making it inert. But then again I have hear of dope ( smack) dealers who keep their stash in the freezer. It did not seem to affect the potency of that stuff.
A word the dope was a powder while in the case of the CWE; the codeine is a solution which may make it more likely to break those ionic bonds of the codeine molecule. I do not know.