Romans says Gentiles can show the work of the law written on their hearts when conscience bears witness to right and wrong. Paul is not saying Gentiles save themselves by conscience. He is showing that all people are accountable before God's judgment.
Romans 2:12-16 compares those with the law and those without it. Paul's point is that hearing or possessing the law is not the same as being righteous before God.
This keeps Romans from reducing sin to lack of information. Paul shows that both Scripture and conscience expose the need for God's mercy.
Read this as part of Paul's courtroom-like argument. The passage explains accountability; it does not create a separate path of salvation apart from the gospel.
Original wording based on Romans 2:12-16.
14(for when Gentiles who don`t have the law do by nature the things of the law, these, not having the law, are a law to themselves,
15in that they show the work of the law written in their hearts, their conscience testifying with them, and their thoughts among themselves accusing or else excusing them)