If at the expiration of said notice, the said owner or owners have neglected or refused to comply with the requirements of said notice and order of said council, it shall be the duty of said council to enter upon the premises of said private cemetery and erect or cause to be erected such fence as shall comply with the provisions of this act, and shall certify the costs of said construction to the city clerk, and said costs shall become a lien against the estate held in such private cemetery and shall be assessed and collected the same as other taxes against real estate in the city wherein such private cemetery is located.