In "The Language of History: Sanskrit Narratives of a Muslim Past", @AudreyTruschke's comments on the six languages (भाषाषट्क) beginning with संस्कृत. She writes that the "sixfold set doesn't admit any vernaculars". What
Jonaraja, the commentator on पृथ्वीराजविजय, writes about the words "षण्णां गिरां" in the poem is simply "षण्णां संस्कृतादीनां वाचां". What 6 languages did Jonaraja have in mind? Let us look at the same Jonaraja's commentary on a verse from a different poem, श्रीकण्ठचरित (25.36)
Mankha in श्रीकण्ठचरित describes लोष्टदेव, a Kashmir scholar thus - वदनाम्बुरुहे यस्य भाषाः षडधिशेरते. Jonaraja, in his commentary, enumerates the 6 भाषाs - संस्कृतं प्राकृतं चैव शूरसेनी तदुद्भवा । ततोऽपि मागधी प्राग्वत्पैशाची देशजेति तत् ॥ देशजा is indeed the vernacular.