When Does "The Animatrix: Beyond" (2003) Take Place?

"Beyond" is a science fiction animated short film written by Koji Morimoto that released June 3rd, 2003. So when is "Beyond" set? 

It takes place on the fictional The Matrix timeline roughly in the years: 

~2700s AD 

We know this because the A.I. antagonists in the story are only partially concerned with the main characters' awareness of the Matrix, so it absolutely cannot be before the feature film "The Matrix Revolutions" (2003), which takes place in 2700 AD. 

It is technically an entirely unplaceable work. All that can be said with certainly is that it takes place after 2700 AD. 

The timeline of the Matrix Universe is fairly unique among the largest franchises because the human characters within its fictional world (diegesis) do not themselves know what year it truly is for the duration of most of the stories. 

The end of the narrative includes a screen showing a phone call tracing program reading, "2-2-03, 15:52". Presumably, this timestamp means the entire story takes place at around the same time on the current calendar within the Matrix: February of 2003 AD. Things appear to be contemporaneous with the making of the work but this timestamp clearly refers only to time for the characters living within the Matrix who accept the false narrative they are presented: that it is still the late 20th century. In the video game "The Matrix Online" (2005), Tic Tock explains that the calendars and clocks within the Matrix are [or maybe previous to the events of the feature film, “The Matrix Revolutions” (2003), when this animated short seems to take place after, were] periodically reset. 

It is (probably) the eighth chronological short film in The Matrix Universe timeline. It can be watched at its timeline point or entirely separately.