Who is obliged to establish righteous courts?

[nehemiah]

The Courts where I live do not enforce all of the Noahide laws. Because of this, I would like to create a new one that does. (Regardless of whether or not I am obligated to do so, I believe that I am permitted to do so, and this is something that I would like to do.)

Are there any special requirements for how a Noahide Court is supposed to operate?

The Court which I propose to create would not be able to enforce judgments of capital punishment due to the existing secular legal system. Is this a problem?