If you look up codeine, or any product derived from codeine (such as hydrocodone, the active narcotic ingredient in Vicodin®) in the Physician's Desk Reference, one thing you may notice is that none of them are available as a preparation for injection. The reason for this is that codeine triggers a massive release of histamine when injected, and this has the potential to lead to an anaphylactoid reaction, which can be rapidly fatal. If this happens, unless you have an injection of epinephrine handy, chances are you will die before help can arrive.
In general, it is a bad idea to crush up pills and inject them. Most pills contain insoluble fillers such as silicates and waxes that cannot be totally filtered out with a cigarette filter. These particles can lodge in capillaries, or carry bacteria deep into organs like the heart and lungs, leading to life-threatening ailments such as gangrene and endocarditis.
In addition to these potentially deadly complications, there is really very little to be gained by injecting hydrocodone rather than taking it orally. The reason heroin is usually injected is because of the intense rush it produces. Injected codeine, hydrocodone, or even morphine will not produce the same effects because they do not cross the blood-brain barrier nearly as quickly as heroin does. So while the effects may come on more rapidly after injecting, you will not get any "higher" than you would if you simply swallowed the pills.
All-in-all, it would actually be safer (and more effective) to inject heroin purchased on the street than any codeine derivative.