Try weaning yourself down..
Do a taper,
Though, I would never recommend Suboxone or Methadone to a codeine user.. Codeine is WAY too weak to get on subs or 'done.
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Just tough it out, Codeine WD's aren't that bad.. of course it's very uncomfortable.. but that's what comes with any addiction.
I quit Hydrocodone cold turkey. a 2 year addiction of using 120mg daily.. I went through hell for 7 days, and felt uncomfortable for another 5-7 days, but felt better after that.. and Hydrocodone is much more potent than Codeine.
Just be glad yo havn't had to go through serious opiate addiction.. opiates such as Heroin, Opana, Methadone, etc.
Trust me, because I'm a current addict.. The superior opiates I listed above are almost impossible to quit cold turkey.. Codeine WD is a walk in the park compared to those.