Creeping Jenny, Moneywort, and a number of other mostly unprintable names, is becoming regarded by many as an invasive plant even though many places sell this as a "fast growing" ground cover. This plant develops a very extensive root system so any covering needs to be such that it keeps any top growth from getting access to the sunlight all plants need for growth. The barrier does not necessarily need to be deep, or thick, just impervious to light. About 6 sheets of newspaper, or one layer of cardboard, covered with something to hold it in place and hide it would be sufficient.
The glyphosate probably will not do a good job of control since this is one of the many plants that can keep that poison from getting to the whole root system. The most effective method of control of this plant is to dig up the root system.