It is only a "system" if it is applied to a large group of such taxa (for example, all the flowering plants).
A system must be taxonomic, that is deal with many plants, by their botanical names.
Although thinking about relationships of plants had started much earlier (see history of plant systematics), such systems really only came into being in the 19th century, as a result of an ever-increasing influx from all over the world of newly discovered plant species.
A milestone event was the publication of Species Plantarum by Linnaeus which serves as the starting point of binomial nomenclature for plants.
By its size this would qualify to be on this list, but it does not deal with relationships, beyond assigning plants into genera.