This will be live by the end of 2019 in a similar form.
The MakerDAO stablecoin system on the Ethereum blockchain produces the DAI stablecoin, with 1 DAI pegged at 1 USD. There's currently $85M of DAI in circulation.
Each $1 of DAI is backed with $1.50 of Ether, the currency of the Ethereum blockchain.
Later this year a major upgrade will go live named "MakerDAO multi-collateral DAI". The "multi-collateral" bit is related to a basket of currencies.
By Q1 2020, the DAI stablecoin will be backed still by ETH, but also backed by USDC (a US dollar stablecoin run by Coinbase), REP (a token for the Augur decentralized prediction market), and other tokens.
Not exactly "a digital currency backed by a floating basket of currencies" but a related concept and in production very soon :-)
https://mkr.tools https://vote.makerdao.com https://makerdao.com