Depending on the facts of the case, your apartment complex may be liable for the damages. It would likely depend if they were negligent in the maintenance and operation of the gate.
Depending on the extent of the damages, you may want to file an insurance claim with your carrier. They may then seek reimbursement from the apartment complex. Alternatively, if the damage is less than $7,500, you may want to file a small claims case.
As you can imagine, an attorney would need to fully understand the facts of your case to be able to advise you, so I would recommend that you speak with an attorney to discuss your options. If you would like a case assessment with our team, please go here to schedule.