The logline is too long and as I read it I asked why must the unite of soldiers stop the other guy? what made them need to do this? Point is the structure of the logline is working against itself so better to put the inciting incident first.
Secondly can you specify a main character? Cold it be the second in command or the unit's sergeant as appose to an arbitrary number of characters?
"...virtually indestructible?" is a self contradicting description, either it is or isn't indestructible. I think it being indestructible provides more of an obstacle for the MC's so better to make it so.
Lastly no need to describe in so much detail the nature of the weapon, its mission or the setting let it all be implied by the character and obstacle descriptions.
My try:
After their commander was mind controlled by the enemy's sentient doomsday weapon a unit of elite soldiers must stop an indestructible spaceship from destroying all of humanity.
Hope this helps.