Judicially is the adverb from judicial. It means “by a court,” “in a court way,” or “as a matter of law and judges.” If something is decided judicially, a judge or a court decided it — not a vote, not a boss, not a rumour. You also hear it when someone is speaking of the proper role of courts: “that question cannot be settled judicially” means the courts are not the right place for it. It is formal. In speech, people more often say “in court” or “by a judge.” Same warning as judicial: this is not “wisely.” That word is judiciously.