Because you're already casting the card using an alternative cost (by casting it without paying its mana cost), you can't pay any other alternative costs for the card, including casting it face down using the morph ability. You can pay additional costs, such as kicker costs. If the card has any mandatory additional costs, you must pay those.

If the card has {X} in its mana cost, you must choose 0 as the value for X when casting it without paying its mana cost.

You must still follow any timing restrictions and permissions, including those based on the card's type.