|I don't know that 14-bit is a video standard but anyway it's going to depend on the screen resolution, the amount of video memory and what the video adapter can provide.|
16 bit color provides 2^16 colors but requires 16 bit (2 bytes) of video ram per pixel. A 640 x 480 screen has 307,200 pixels so it needs 614,400 bytes of ram or 600 K. An 800 x 600 screen has 480,000 pixels and needs close to a meg of ram. That's not much, at least by today's standards but note that not all video memory goes toward displaying colors. I'm just pointing that out to show that sometimes reducing resolution will allow more colors to be displayed.
If that old laptop shares video video memory with system ram you'll want that shared figure to be pretty high. You'll need to make sure you have the most updated 98 video drivers installed. That's the most you can do. If after doing all that you still can't get 16-bit, well, you're out of luck.