Would you call the character of Doctor Faustus heroic? Give reasons for your answer.

Doctor Faustus isn't a hero. He performs no heroic deeds and, in fact, bargains away his soul for an eternity for a short time with more power. He is the protagonist of the story and perhaps the hero of his own story, but ultimately, Doctor Faustus is a tragic character and a serves as a moral warning to the audience.
Faustus's actual goal is to have godlike powers. He doesn't pursue necromancy to bring back a lost love or to right some wrong; he does it for his own pleasure and for the power he believes he will get. For the same ends, he bargains his own soul for 24 years of power.
He rejects the advice of a good angel and instead listens to demons like Lucifer and Mephistophilis. He doesn't use his powers for any good: he uses them to create mischief. At the end of his life, he receives a warning to repent and rejects it. Faustus is decidedly unheroic and serves as more of a cautionary tale to those who might seek power and pleasure over more holy pursuits.