Mijjn is a Japanese agency developing a private blockchain based on NEM protocol. There is no currency behind mijn so this is why it's not a well know one.
Recently they offered 4 cloud server instance for the companies interested to test their blockchain, with the support form Sakura, a leading internet cloud service provider, and Tech Bureau, a fintech and cryptocurrency solutions company.
Tech Bureau announced the first blockchain use case for a division of the Japanese Ministry of Agriculture, Forestry and Fisheries. They are building a supply chain and distribution channel on a blockchain for the Japan Gibier Promotion Association. The blockchain has to comply with Japanese distribution standards and aims to ensure quality food for public health.
Japan seems to be very friendly with blockchain technologies. They recently endorsed 11 Cryptocurrency Exchanges, Aiming to Become Bitcoin Powerhouse.
Source: http://mijin.io/en/992.html