The “righteousness ” that Jesus had in mind is the quality of doing what is right by conforming to God’s will and commandments. The psalmist said that he was “crushed with longing ” for God’s righteous judicial decisions.
وَٱلْأَخُ ٱلَّذِي يَبْتَغِي مَسْؤُولِيَّةً فِي ٱلْجَمَاعَةِ لَا يَتَأَهَّلُ لَهَا إِذَا ٱمْتَلَكَ هذِهِ ٱلصِّفَةَ .‏