Here is the card padlock and matching key card for it.

Here is a close up view of the keycard, along with explanantion of the code.

And Info on disassembling the card padlock, if you ever wish to do so.

Now for some insides of the lock.
(The top piece has notches in it that prevent the lock from opening if the holes in the card are too big for the pin. (The top half is shown on the right.))

Here are the pin/spring assembly removed from the lock. (I intentionally rekeyed this lock, to work with the existing keycard, unfortunately, I had to remove one of the pins/springs, to do this, as the original key card did not have the same digits as the key card this lock was rekeyed for. (And I ended up losing that pin. There should be 4 of them in a normal case of disassembly.))

Another of the pins, closer up.

Lock disassembled one step further. Here, If the holes are too small for the pins, then the bottom piece prevents the lock from opening with that card.

Overall. Picking this type of padlock should be possible. It would just be a matter of applying tension to the lock pin sliding assembly, and using a pick to set the 4 pins to the correct heights. (I haven't managed to pick this yet.) This lock is most likely able to be opened using padlock shims.;
(I did at one point use this lock for my high school locker. The only problem was that I would once in a while forget the key card for this lock, and even came really close to having it cut off altogether because of that.)