I have added a PhaseListener to faces-config.xml:
com.project.NotificationListener>
Before JSF 2.2, PhaseListeners are not registered as CDI injection targets. Using @Inject (and @EJB) has effectively no effect in PhaseListeners. You'd need to manually grab the CDI managed beans by programmatically evaluating an EL expression referencing the @Named's (implicit) name, or as last resort via JNDI and BeanManager which is quite clumsy.
So, if you can't upgrade to JSF 2.2 (which should be compatible with any JSF 2.0/2.1 and Servlet 3.0 compatible web application), then your best bet is programmatically evaluating an EL expression referencing the @Named name. Assuming that you've a
@Named("stuff")
public class MyCDIStuff {}
then this should do:
FacesContext context = event.getFacesContext();
MyCDIStuff stuff = context.getApplication().evaluateExpressionGet(context, "#{stuff}", MyCDIStuff.class);
// ...