That is basically a 33 x 34 foot basement. If you have the time and a couple of picks and shovels the hole is free. The rest is open to debate depending on different factors. Remember California has the “earthquake code” that MUST be considered. Then you have the type of walls you will build, in accordance with the code. How thick will the walls be? What material will you use? Will you use any type of seismic abatement ‘shock absorbers’? Will you have to build columns to support the upper structure? How much of an upper structure will you have? (The taller you go the more support you need). Will the ceiling be wood or steel beam construction? Will Palmdale have any EXTRAS to the building codes that might prohibit this from being built or raising the cost? Remember that Palmdale is more active seismically than many other areas of California.
I’m sorry I can’t give you a better answer, but at least you have a better idea as to what you face. If you were away from prying eyes you might be able to build it without anybody knowing about it officially. But you still need to consider the earthquake code.