Unless another nominated executor qualifies within the time provided in Code Section 53-6-11, the probate court shall appoint an administrator with the will annexed of a testate estate when:
(1) No executor is nominated in the will;
(2) The nominated executor has not reached the age of majority, to
serve until the disability ceases;
(3) The executor dies, resigns, or otherwise becomes disqualified to
serve; or
(4) A testate estate is unrepresented for any other reason.