"When a Pokémon holds an Enigma Berry and is hit by a super effective move, it will recover ¼ of its HP. This effect is in Generation IV only."
Enigma berry only works when the pokemon survives the hit. It's the same principle with Sitrus berry, which only activates when your health falls to a certain level, but it won't activate if you faint. The pokemon has to survive the hit if you want Enigma berry to activate.