I'll quote my answer on other post about the same problem.

My friends and I had the exact same problem (Usually around Gridania) until we tried something I saw in this forum.

Go to FFXIV Config and set the following:

-Video Settings

Multisampling-> 2x MSAA
General Drawing Quality -> Standard
Background Drawing Quality-> High

-Graphics

Texture Quality -> Standard
Texture Filtering-> Standard

-----------------

After doing this the Directx Error never appeared again. It's not really a matter of lowering the graphic quality.
My friend's computer has that exact configuration and he even had the Multisampling off (meaning it was lower than what I listed) after he put it on 2x the problem was fixed.

Try it, the Standard quality textures are almost the exact same as the High ones, you will basically notice the Item/skill icons being less defined.

If it fixes your problem reply here so other players will know if it might work for them.