Tylenol with codeine tablet #3 contains 325 mg APAP (Tylenol,) and 30 mg of codeine. Tablet #4 contains 325 APAP and 60 mg of codeine. Most generally any medication maybe crushed and then snorted; however, the damage to your nasal cavity / sinuses is the main complication.
Snorting ANY medication will cause it to act quicker due to the absorption happening in the mucus membrane and sinuses. These will place the drug on a fast track into the blood stream due to the blood oxidization process. The stomach will take 30 minutes (at least) to pump it into the blood stream through absorption, and about an hour for full effectiveness.
My suggestion (assuming the need is for immediate relief of more severe pain,) is that you take 1-2 tablets (depending on your approved dose,) and crush them into a fine powder. Then mix the powder with milk, make sure you ingest all of the medication as it will commonly stick to the glass walls. The physiology behind this is that milk is absorbed very quickly by the stomach wall; particularly via a specialized channel. Note that simply placing the powder into your mouth will also work, but will take a little longer for full effect.
The down side is that the medication is not slowly put into your system; therefor it will not last as long.
Long story short, let your stomach do the work and give your nose a break (there as sooooo many complications snorting anything that's not specifically meant to be.)