Using results of current experiments in silanization, how to achieve a higher contact angle?
It's always good to clean glass surfaces with oxygen plasma or UV ozone treatment before silianizing, but 108° is pretty good with an alkylsilane.
The best you will be able to do with this type of surface treatment is using fluorosilanes.
Silanization agents are basically made of three parts, a functional group, a linker and a coupling group:


The coupling group is what allows the silane to attach to a surface and is found bound to the silicon atom.
Typical couplers are hydrolyzable groups like alkoxy, acyloxy, or halogen.
These don't generally influence the hydrophobicity of the resulting surface directly, though they will affect how well the silane adheres to a given surface, the manner and speed with which it can be applied, and the deposition density.
Alkoxy and acyloxy groups can be applied from aqueous solutions and are generally less reactive, but halogen groups can be deposited from anhydrous solvents or the vapour face quite quickly.
The linker is typically just a short alkyl chain between the silicon atom and the functional group to reduce steric interactions between adjacent silanes.
The functional group is what has the greatest influence on hydrophobicity.
Many different functional groups can be added, some even conferring hydrophilicity instead, if desired.
In general, longer alkyl chains are more hydrophobic, but long fluoroalkane chains are the most hydrophobic and will also not interact easily with organic solvents either so fluorosilane coated surfaces are often known as omniphobic by virtue of being both hydrophobic and oleophobic.


So if you want the maximum contact angle possible from a simple surface treatment, you're looking for something like 1H,1H,2H,2H-Perfluorododecyltrichlorosilane.
It may also be possible to simply spin or spray coat a fluoropolymer like Teflon AF or Fluoropel, depending on your application and surface. All these types of coatings will give contact angles up to about 120° in the best case and to get any higher will require surface patterning to achieve superhydrophobicity.