IVing codeine is not a good idea, but neither is it as dangerous as some here will have you believe. Medical sources often suggest slow infusion of IV codeine rather than bar it outright.
Still, it is NOT A GOOD IDEA, for two reasons. As quale said, codeine is quite effective at provoking a histamine response, and two, it must be metabolized to morphine to have an effect.
I have personally IV'd codeine, out of curiosity, and it was quite unpleasant. Instead of a normal rush I got a rush of allergy symptoms -- mild swelling, extreme itchiness, weird tingling in my hands and feet. The good, opioid effects didn't kick in for ~20 min or so. IV codeine is unpleasant and useless, stick with oral or IM if you must.