The Patimokkha is one of the books of the Vinaya, i.e. the rules or code of conduct for monks.
There are English-language translations of (introductions to) the Vinaya here, for example The Patimokkha Rules Translated & Explained by by Thanissaro Bhikkhu.
Dozens of suttas (e.g. SN 56.9) use the word dhammavinaya, translated as teaching and training and/or Dhamma and discipline.
You might like to read the original version of this dictionary entry on the Buddhavacana web site -- it contains hyperlinks to to parts of the various suttas which it references:
training in higher virtue. A definition is given by the Buddha at AN 3.90. It consists of a thorough undertaking of the Pātimokkha's rules.
- Adhi·sīla·sikkhā is one of the three sikkhās, together with adhi·citta·sikkhā and adhi·paññā·sikkhā. It is said of these three trainings at AN 3.82 that they are 'ascetic tasks of an ascetic' (samaṇassa samaṇa·karaṇīyāni), at AN 3.93 that they are 'urgent tasks of a bhikkhu' (bhikkhussa accāyikāni karaṇīyāni), and at AN 6.30 that they constitute the 'supreme training' (anuttariyaṃ sikkhā) for the purification of beings, etc. (formula in the style of the Mahāsatipaṭṭhāna Sutta)
- They can even replace the Pātimokkha, in some cases (AN 3.85).
- However, adhi·sīla·sikkhā is not only for bhikkhus, since it should also be undertaken by upāsakas, as they meet with their success (sampadā) or their prosperity (sambhava), lest it is their their failure (vipatti) as in AN 7.30, their decline (parihāna) as in AN 7.29, or their ruin (parābhava) as in AN 7.31.
AN 7.29 through AN 7.31 says that lay followers (upāsakas) too should practice "higher virtue", but don't define it.
I suspect that "higher" virtue means more than the five precepts.
Maybe in AN 3.85 it's used instead of a detailed set of rules and definitions, and is used with "heightened discernment" (i.e. when you discern what's what, whether something is virtuous and skilful): in summary, "abandon the three poisons, don't do anything unskillful or engage in any evil".