Back further than you'd expect. These folks (The Mummies Of Urumchi) had tartan too.
Dating as far back as 4,000 years, they were made by accident--naturally--by the dry climate in the salty Tarim basin. The oldest mummies from Cherchen found so far died about 3,000 years ago, while the oldest mummies found near Loulan died about 4,000 years ago.