The issue is obvious. You said your initial solution was about 260mL of water. As codeine is completely water soluble, it will distribute evenly throughout the volume of water in which it is dissolved in. Now, if your solution after filtering was only approximately 20mL, then you are effectively obtaining 20/260 or 1/13 (one thirteenth, less than 10 percent) of the codeine that you originally dissolved.
The reason that you ended up with only ~20mL of water is because you are using an ibuprofen/codeine combination. From experience, I have found that both N+, and the generic equivalent manage to soak up a large amount of the water in the clumpy insoluble paste. The only way to avoid this is to use a relatively large volume of water in comparison to what you would use for a paracetamol/codeine combination, and then apply excessive squeezing to the filter to ensure that the filtrate does not feel wet or paste-like - completely dry isn't likely but squeezing until the water starts dripping slowly is plenty. You have to be careful so as to not break the filter from the pressure of squeezing. Essentially you want to have about 90% of the inital amount of water you started with.
Another method of extracting ibuprofen/codeine tablets which I've found to be quite successful is doing multiple smaller amounts of pills, like perhaps 2x15 or 3x10 tablets so that there isn't such a large clump of paste going into the filter. Some squeezing is still required with this method, however it is much less.
The amount of water that you used is more than enough - I would use about 150mL total for an extraction of 30 ibuprofen/codeine tablets. You really only need to put enough water so that it's not a paste, its liquid enough to stir the solution so as to ensure to dissolve and distribute the codeine. You don't need to be as careful with using larger volumes of water with ibuprofen containing products as ibuprofen is basically completely insoluble and would take literally litres of water solvent to allow a damaging amount to dissolve.
These days I generally opt for using ibuprofen containing products as 1) they're cheaper and 2) there is less potential for harm due to ibuprofen being relatively insoluble - paracetamol is slightly water soluble and over time using it quite often can cause complications which I am not prepared to experience if it can be avoided.
If any of this is unclear, feel free to ask any questions.