Both the headword (which must be quoted from somewhere: see below) and the gloss are nominative/accusative neuter singular. The entry = Synagoge delta391; Photius, Lexicon delta801. Its immediate origin is doubtless Hesychius delta2533: dusaxqe\s: baru/.
That entry in Hesychius is considered by Latte a Cyrillian interpolation, which is probable enough if one considers that the same gloss occurs (according to Latte) in two Cyrillian codices still unpublished: Laurentianus 57,39 and Coislinianus 394. On the other hand one should take into account the fact that this adjective is unattested until the second century AD -- when we find it in Maximus Astrologus (in reference to illness), in Aretaeus (medical literature), Tryphiodorus (poetry) and Cyranides (magic); also that Hesychius' sources, through Diogenianus and others, are mainly writers of the classical and Hellenistic periods.