Just do the math:

4 Bytes (size of var) * 16384 * 16384 * 2 = 2147483648 Bytes = 2 GB

Since Acknex is a 32 Bit programm thats exactly the maximum number of ram it is allowed to use.
(Source: http://msdn.microsoft.com/en-us/library/windows/desktop/aa366778%28v=vs.85%29.aspx#memory_limits)
However, it also needs space for other variables so it runs out of ram (no matter how much physical ram you have in your computer).

I'm afraid an image wouldn't be any better.
If you REALLY need this much data, save it on the hard drive in a fitting format and dynamically load only the few MB you currently display.