I have an alarm system in my home covers doors/windows, just breaking. I have recently had someone in my home. Couple small items were taken, just nuf to make you think they weren't missing but... I had keys missing and thought I lost them somewhere but they were lost on condo community property. Isn't there a computer gadget that can be bought that can access your security code from the panel by holding it next to it and it would give you sequence of numbers to enter so alarm doesn't go off? I have seen it done but can't remember what it is. The person I suspect is a computer junkie and can write code, so don't think it would be beyond his capabilities, he does it for a living. I want to present some evidence of what I'm talking about to someone who can take this further.
I am also going to contact police computer crimes division to further this question. Telling someone what happened makes someone who isn't computer sophisticated look at you with raised eyebrows.

They can not access the code by just placing it next to the key pad unless someone is pushing the numbers. If it is a wireless system, they may pick up signal though a receiver. But anyway there are also 100's of ways to break into a home with a security system. Do you have cameras that record in the home, do you have motion detectors ?

Your system may have an event log that will tell the time of arming and disarming of the system and zones violated. It would also tell which user, if you saw your user code used when you at work? you would know it was someone that knew your code(Maybe seen or heard you say it).
If you can tell which system and if wireless, may be able to give you more ideas.

You mention doors and windows only for break in. If 1 door or window is jumped or bypassed, it would be vulnerable.
You should also have a Motion detector(s), there are also mats, beams among other sensors to protect from Breaking.
I went to a House to get a system back operational, the guy was a Billionaire, but for what ever reason the Big Miami company installed contacts on ALL doors, except 1 Back door. No interior motions, Nothing, which means someone can enter the house, empty it, and go undetected.
I found it when doing testing of each zones. Some Techs will assume a ready light means all zones are secure. They focus too much on the Monitoring Contract.

While there are sophisticated devices that could possible detect your code under certain circumstances. They are not likely to be in the hands of someone who might take just a few items or use keys that you misplaced.

Check out what Stratmondo suggested about a log of access times. That may be the only way to prove that your alarm was disarmed when you didn't do it.

Otherwise, you should take pictures and/or video of your home. Then you would have proof if anything is missing. Also, you should change the locks (when ever you lose keys) and change the access code regularly.