If 70 m is the diameter, not radius, that area is a factor of 4 too high. Should be more like ~3850 m^2. Still physically impossible at that size but it does make the required size a bit more tenable.
Antennas at Goldstone Deep Space Communications Complex
Name Diameter Description
DSS 12: "Echo" 34m Decommissioned in 2012.
DSS 13: "Venus" 34m Beam waveguide antenna (BWG) on altazimuth mount, located in Venus, California. ~910 m2 aperture.
-> DSS 14: "Mars" 70m Cassegrain reflector on Alt/Az mount. ~3850 m2 aperture.
DSS 15: "Uranus" 34m "High Efficiency" reflector on Alt/Az mount
DSS 24, 25, 26: "Apollo" 34 m BWG reflector on Alt/Az mount
DSS 27, 28: "Gemini" 34 m BWG reflector on "High Speed" Alt/Az mount
https://www.jpl.nasa.gov/news/nasas-deep-space-network-looks...
As a sanity check, the video says the area of the dish is approximately one acre which would be ~4,046m2 and a 35m radius disk is ~3,850 m^2.
This works out to roughly 0.7 acres.
I had to look it up to check: my mental model was that a foot is some king's foot but there is more of a storied history.