Absolutely, definitely not. Works are important, but we are not justified by works.
The Catechism states this unequivocally:
161 Believing in Jesus Christ and in the One who sent him for our salvation is necessary for obtaining that salvation.42 “Since ‘without faith it is impossible to please [God]’ and to attain to the fellowship of his sons, therefore without faith no one has ever attained justification, nor will anyone obtain eternal life ‘but he who endures to the end.’”
42 Cf. Mk 16:16; Jn 3:36, 6:40 et al.
We are not justified by slavishly following the Law (which is what “not justified by works” is saying) — we are justified by faith, and that faith will transform our lives with the fruit of the Spirit which pervades every act so that our works show that we are justified.
Matthew 5:16 — Let your light so shine before men, that they may see your good works, and glorify your Father which is in heaven.
Peter wrote of this in 2 Peter 1:
1 3 His divine power has given us everything we need for a godly life through our knowledge of him who called us by his own glory and goodness. 4 Through these he has given us his very great and precious promises, so that through them you may participate in the divine nature, having escaped the corruption in the world caused by evil desires.
5 For this very reason, make every effort to add to your faith goodness; and to goodness, knowledge; 6 and to knowledge, self-control; and to self-control, perseverance; and to perseverance, godliness; 7 and to godliness, mutual affection; and to mutual affection, love. 8 For if you possess these qualities in increasing measure, they will keep you from being ineffective and unproductive in your knowledge of our Lord Jesus Christ. 9 But whoever does not have them is short-sighted and blind, forgetting that they have been cleansed from their past sins.
Peter deliberately lists the fruits of the Spirit. In "making every effort" to add those virtues to faith, Peter is saying "allow the Spirit to do his work" because a living faith will engender good works (cf James 2:26). Any effort we bring to bear for ourselves is using our conscience to do good works. Verse 4 says that we participate in the divine nature by virtue of God's great and glorious promises. This means that it is necessary that we believe those promises will be fulfilled: this is faith.
This is not to say that good works are not inherently good! They point towards — and ultimately come from — God, as Pope Francis and Pope Benedict XVI have pointed out. One's conscience is God-given, formed by the natural Law, and in doing what we inherently perceive to be good we are allowing the Spirit to work in our lives.
But we are saved by faith. That is all that is necessary. Everything else comes from faith.
You may recognise some of this as coming from another answer to a very similar question.