Can a modern washing machine pump high enough to reach a sewer line that's 43" above the ground?
No.  Well maybe it can, but it shouldn't.
RTFM
If you check the documentation that came with the washer, it should contain the maximum drain height.  Generally, the maximum height is around 39&quot; (99 cm).

Newer washers often have a drain hose permanently attached, which is designed to make drain installation fool proof. The supplied drain hose shows you exactly how high the washer can discharge.
Raise the washer
Depending on the machine, and whether or not you're already using a pedestal.  You may be able to raise the whole machine up, to accomplish what you want.  The maximum height is not height above sea level, it's height above the bottom of the washer. So if it's possible to do so, raising the machine up a few inches (safely) might be the solution.
If it's a front loading washer; and you're not already using a pedestal, you may be able to purchase (or build) a pedestal to raise the machine up.  If not, you may want to think about building a raised floor to raise the whole area up.
Keep it up to code
International Residential Code (IRC) says.

International Residential Code (IRC) 2012
Chapter 27 - Plumbing Fixtures
SECTION P2706 WASTE RECEPTORS
P2706.2 Standpipes. Standpipes shall extend a minimum of 18 inches (457 mm) and a maximum of 42 inches (1067 mm) above the trap weir. Access shall be provided to all standpipe traps and drains for rodding.

Which means if you connect the drain hose to a standpipe, the standpipe has to be at least 18&quot; above the point at which water will begin to flow from the trap. So your 43&quot; height, could quickly become 61&quot;.