Proverbs 21:21- Whoever pursues righteousness and kindness will find life, righteousness and honor.
Those who pursue righteousness not only find righteousness but they also find honor and life. So, when seeking after righteousness, God doesn't give us only what are seeking, he gives more that. We are well rewarded when we seek after Godly characteristics.
But our own righteousness cannot get us into heaven, only the Righteousness of Jesus can, for ours are like filthy rags. How do we get this righteousness? Jesus had to wash away our sin with his blood in order to count to us his righteousness so that we would be blameless in God's sight, that is so humbling.