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.