2-4-711. Appeals -- staying agency decision. An aggrieved party may obtain review of a final judgment of a district court under this part by appeal to the supreme court within 60 days after entry of judgment. Such appeal shall be taken in the manner provided by law for appeals from district courts in civil cases. Unless otherwise provided by statute or unless the agency has granted a stay through the completion of the judicial review process:

(1) if appeal is taken from a judgment of the district court affirming an agency decision, the agency decision shall not be stayed except upon order of the supreme court; except that, in cases where a stay is in effect at the time of the filing of notice of appeal, the stay shall be continued by operation of law for 20 days from the date of filing of the notice;

(2) if appeal is taken from a judgment of the district court reversing or modifying an agency decision, the agency decision shall be stayed pending final determination of the appeal unless the supreme court orders otherwise.