Appellate review may be sought as in other civil cases: PROVIDED, HOWEVER, That review must be sought within fifteen days after the date of entry of the judgment of the superior court. The supreme court or the court of appeals, on such appeal, may change, confirm, correct or modify the values of the property in question as shown upon the roll. A certified copy of any judgment of the supreme court or the court of appeals shall be filed with the county auditor having custody of such roll, who shall thereupon change, modify, or correct such roll in accordance with such decision if required.