This headword, h(goumeni/a, according to H.Stephanus is "dignitas abatis", the rank of an abbot (h(goume/nos, eta 72). The term, although used exclusively in the Byzantine age, is to be found in Herodian, who likewise advocates its spelling with diphthong (i.e. rather than h(goumeni/a).
The entry is taken from the Ambrosian Lexicon (Ambrosianus 37, but not in Laurentianus 59,16); perhaps originally from Herodian, Partitiones 45 or 221.