SpaceX's billionaire founder, Elon Musk, gave attendees at the South by Southwest festival in Texas the first public look at the fourth flight test carried out by his company's reusable self-landing rocket, nicknamed the Grasshopper.

This latest "hop," conducted on Thursday at SpaceX's rocket test facility in McGregor, Texas, sent the Grasshopper twice as high as it ever went previously: In a statement, the company said the 10-story-tall rocket rose 24 stories off the ground (262.8 feet, or 80.1 meters), hovered for 34 seconds and landed safely on its own.

"Grasshopper touched down with its most accurate thus far on the centermost part of the launch pad," SpaceX said. "At touchdown, the thrust-to-weight ratio of the vehicle was greater than one, proving a key landing algorithm for Falcon 9."

Thursday's test builds on test flights conducted last September, November and December. During his keynote address at the annual SXSW gathering in Austin on Saturday, Musk joked that this flight was the "Johnny Cash hover slam," according to an account from NewSpace Journal. Johnny Cash's song about a "burning ring of fire" was playing in the background as the video rolled.

Grasshopper's vertical-takeoff, vertical-landing technology is considered a key part of SpaceX's plan to make its Falcon 9 rockets more reusable. "With Grasshopper, SpaceX engineers are testing the technology that would enable a launched rocket to land intact, rather than burning up upon re-entry to the Earth's atmosphere," the company said.

A Falcon 9 rocket delivered an unmanned SpaceX Dragon capsule safely to the International Space Station last week, and that capsule will soon be filled up with more than a ton of cargo for return to Earth. Eventually, SpaceX plans to refurbish Dragon capsules as well as Falcon boosters for reuse, but the company hasn't gotten to that stage yet. NASA has contracted with the California-based company to make 12 Dragon deliveries over the next several years at a cost of $1.6 billion. The current cargo mission is the second under the terms of the contract.

Looking further ahead, SpaceX aims to adapt its boosters and crew vehicles to send astronauts to Mars. The 41-year-old Musk told the SXSW crowd that he might well end up being one of those astronauts. "I've said I want to die on Mars," CNET quoted him as saying. "Just not on impact."

Update for 7:45 p.m. ET March 9: At about the 1:15 mark in that video, you might notice a dummy cowboy standing on the rocket. That's not the first time a ringer for a wrangler has taken a ride on the Grasshopper.

More about SpaceX and Mars:

• Elon Musk wants 80,000 of us on Mars
• SpaceX aims for fully reusable rockets
• SpaceX chief plans to be spaceflier, too

Alan Boyle is NBCNews.com's science editor. Connect with the Cosmic Log community by "liking" the log's Facebook page, following @b0yle on Twitter and adding the Cosmic Log page to your Google+ presence. To keep up with Cosmic Log as well as NBCNews.com's other stories about science and space, sign up for the Tech & Science newsletter, delivered to your email in-box every weekday. You can also check out "The Case for Pluto," my book about the controversial dwarf planet and the search for new worlds.