What combination length best secures my key safe? I have the following key safe and need to decide upon a combination for it.

It's fairly simple mechanically with these features:-


*

*It allows the characters 0-9 and A and B (12 possible digits in total). 

*The combination can be 4 to 12 characters long.

*Each button can be used only once.

*A weirdness is that the buttons can be pressed in any order for the same code, so 1234 is the same code as 4321. 

*Once you've entered the correct code, you turn the knob to open the safe.  It doesn't spring open immediately upon correct code entry.


From the manufacturers website FAQ:-

"The C500 Police approved key safe has 4,096 possible code combinations"

It seems to me that the security /difficulty of the combination will depend on how many digits I set, but I can't figure out how many is best. Intuition suggests to me that the longest possible code is the most secure.    But. Clearly if it's 12 digits long, and they're identical in any order, there can only be 1 combination that's 12 characters long. That's not good.  Any ideas? 

There are $4096$ subsets of the twelve element set of possible keys. That's the number advertised - it's not quite right since it includes keys with fewer than four elements, but that's not very many.
The length of the key is really part of the key since when you turn the knob and it fails you have to start over.  That means there's no advantage to choosing the length for the maximum number of possibilities (that would be $6$).
You could argue that short codes are easier to test by brute force (there are "only" $495$ of length $4$) and that someone trying to break in systematically would try them first since they are easiest to type.
