Yet call not this long life ; (line 9)
The end of the poem anticipates an objection every reader of this poem thinks at some point: impossible. This guy is old enough that he could have been one of Socrates's students in Ancient Greece. The speaker tells us that we have the wrong idea if we think that he is just old.
by being dead, immortal (line 10)
The speaker is not old, because he is dead. To be both "dead" and "immortal" is a total oxymoron, or contradiction in terms. Immortality means that you can't die. To make this contradiction work, the speaker has to fall back on supernatural language: he's a ghost.