I have preached righteousness in the great congregation: lo, I have not refrained my lips, O LORD, thou knowest. I have preached righteousness - I think it best to refer these words to Christ and his apostles. In consequence of his having become a sacrifice for sin, the Jewish sacrificial system being ended, the middle wall of partition was broken down, and the door of faith, the doctrine of justification by faith, opened to the Gentiles. Hence the Gospel was preached in all the world, and the mercy of God made known to the Gentiles; and thus righteousness - justification by faith, was preached in the great congregation - to Jews and Gentiles, throughout the Roman empire.
The great congregation, both in this and the following verse, I think, means the Gentiles, contradistinguished from the Jews.
The word righteousness means the plan or method of salvation by Jesus Christ - God's method of justifying sinners by faith, without the deeds of the law. See Romans 3:25-26 (note), and the notes there.