You can get through with no mods - I did the same. Google it and see if you can find the video guide to get through locked doors. Basically it involves dropping your gun into the door and it glitches and opens a fraction. It took me LOADS of times to get it right and for it to let me squeeze through, but you could get lucky first time. Gauss gun worked best for me.
As fish99 said, it's definitely worth it for the level after that.
I've had that happen. I somehow managed to fall though the floor, and landed in one of the final rooms. Won't say which as I don't want to spoil anyone's games. But I would say if you got to the end and you didn't have the decoder, just go though it again, it's well worth it
