Get chaingun/backpack in Doom 64 map 14, Eye of the Storm:

From your starting position at the beginning of the level,
look for the 2 stairways that lead up out of the water.
The backpack sits on a battlement to the right of the
right-hand stairway, the chaingun is on a battlement off to
the left of the left-hand stairway.

To get to either battlement, go up the nearby elevator so
that you're on the highest level above it.  From atop the
elevator you can Run (remember your Run or Speed button) to
jump to the chaingun/backpack.  Note however that you only
have a moment to do so before the elevator drops back down
again.  As such, you may find it easier to back up onto the
elevator so that you're already facing toward the object
when the elevator reaches its highest point.

An alternative method is to ride the elevator up, then step
up onto the nearby wall, and run along the wall to jump to
the chaingun/backback.  The surest but trickiest way to do
this is to Strafe-Run, using a simultaneous combination of
Run-forward plus Sidestep.  This moves the player character
at an odd angle, but is a bit faster than normal running.