It seems Gdiplus doesn't support any 64-bit operations. An somehow easy way to still be able to use Gdiplus methods would be to split the image in two 32-bit images and operate on them seperately.
You could either split the ARGB channels into AARR and GGBB or use two 32-bit images with the lower and higher ARGB bits.
Both variants would need that you either write wrapping functions or split each call into two parts like this:
// This is what you want to do (ARGB, 16 bit per channel)
// g.DrawLine(new Pen(Color(0, 65535, 1024, 31), 1, 0, 0, 100, 100);
// AARR GGBB variant
gAARR.DrawLine(new Pen(Color(0,0,255,255), 1, 0, 0, 100, 100);
gGGBB.DrawLine(new Pen(Color(4,0,0,31), 1, 0, 0, 100, 100);
// ARGBhigh ARGBlow variant
gHigh.DrawLine(new Pen(Color(0,255,4,0), 1, 0, 0, 100, 100);
gLow.DrawLine(new Pen(Color(0,255,0,31), 1, 0, 0, 100, 100);
Note that I used Color(A,R,G,B) order here and I'm not sure about it. According to the MSDN documentation, this must be changed to Color(R,G,B,A) instead. If you won't need the alpha channel, you should prefer the highlow variant as you should still be able to use Color(R,G,B) with it.
To display or save the results, you'll need to merge the 2 buffers.