I have no injector Pulse ever since I had a key made because I lost all keys

Not really. If they erased all the keys, it wouldn't allow any activity, no starter or fuel system.
If they made a new key that worked in the locks it still wouldn't activate the starter as it isn't in the system. Normally on a BMW though you cannot just add in a key that didn't come from BMW themselves. They use an odd system where they program in a secret code into the system and that code allows the use of up to 6 keys that have a specific transponder chip in them. Those particular chips are only available through the supplier for BMW and are not in generic keys. If all of those keys are lost, then you have to replace the immobilizer module itself and get the new "secret code" through a dealer who then activates both vehicle access modules at the same time using a security code from the factory. Then you get two new keys with the option of four more with the new module. This is a case where only a dealership is likely to be of help because you need their security ID and company access to enable the modules. A local smith can cut a key that will work for the locks and turn the ignition, but it won't do much else.