You were right in your doubt. The medication listed is not a barbiturate, a barbiturate is used as sedatives or anesthetics, and is the standard for overdoses. However, it can kill you. But that shouldn't be a standard, tons of things can kill you, but are violent, or high risk of failure. Minocycline is a bacterial antibiotic. It is possible for it to cause Toxic Brain Injury, depends on the drug's effect on the nervous system, and if it causes the body to stop getting oxygen to the brain. The chance is really low. Antibiotics are not as psychoactive as opiods. So it's a lesser chance of oxygen deprivation. It usually just affects the Liver if survived.
Please note, I don't know shit medically, all of this is from 15-20 minutes of research into causes of toxic brain injury, and the drug mentioned. Do not take this as medical advice.