You'll be relatively safe.
60mg codeine is quite a small dose. Idk what you're expecting to feel with that.
When I used to take codeine it'll be 300mg. I once took 10mg Valium with it and it still didn't make the experience good. I've quit codeine due to its weakness now.
If you're mixing benzos and opiates then don't exceed 0.5mg of your Klonopin. If you plan on upping your codeine dose then do not exceed 150mg.