Yes, it is from Heinlein. The title is "Gulf."
The action takes place between the earth and the moon. It culminates not so much in a battle as an undercover mission to stop the baddy from destroying the earth.
It isn't so much a war as that the good guys (and gals, the women play important parts) are trying to keep random bad guys from destroying humanity.
The good guys are ALL brilliant. The ability to learn the artificial language is by itself an indication of superior development as it can only be learned and used by people with extremely high intelligence. The language itself consists of letters that amount to syllables in a regular word. A full sentence in english could be expressed as a single word in speedtalk (the name of the artificial language.)
The idea of speedtalk comes from some mistaken ideas that were popular at the time the story was written. The idea was that thought occurs in words, so a faster and more precise language would lead to faster and more correct thought. The idea originated with (or at least was propagated) by Alfred Korzybski. His works also inspired the "World of Null A" stories by A.E. van Vogt. Also interesting stories. Hoky space opera to distract you from noticing how you are being brought to contemplate the essence of thought and sanity.
The gulf in the story is the (figurative) gap between the average person and the coming generations of geniuses.
The goal of the good guys is to keep humanity from destroying itself before it can make that next evolutionary step to where everyone has the abilities they do.
Very good story.
The " horticultural society" joke in the story is pretty funny. "We weed people."