I thought it are glycosaminoglycans and proteoglycans but it would be interessting to know exactly which proteoglycans and glycosaminoglycans are the most important and which genes encode these molecules/enzymes.
It depends on the basement membrane that you are looking at. Each type of basement differs as to specifically the exact PG and GAG that it contains. So those tend to be BM type specific. BMs are tissue specific and thus are meant to function differently depending on the tissue in which it's found. Thus, the specificity of the GAGs and PGs differ depending on tissue function.
The stromal ECM (rather than basement membrane) will typically be more relevant to the compressive resistance of a tissue, and you are correct that the GAGs are the primary reason for this. GAGs like hyaluronic acid, and chondroitin sulphate proteoglycans bind water, which is what gives non-mineralized tissues their ability to resist compression (as well as many other important properties). There is enormous variation within GAGs, and the specific composition (e.g. number of disaccharides in each chain, sulfation status, etc.) of GAGs in a given matrix will be both unique and difficult to determine.
The protein cores of proteoglycans are encoded by genes like any other protein, but the addition of the polysaccharide side chains occurs in the golgi; they then exit the cell via the secretory pathway. Hyaluronic acid is synthesized by a set of integral membrane syntheses (Hyaluronan synthase 1, 2, and 3), which actually synthesize the polymer on the inner surface of the plasma membrane, from which it is transported into the extracellular matrix via ABC transporters.
Bryan Douglas Crawford thank you very much for your comment. That's also what I thought and supports my guess. We have a case here that you might be able to help with your knowledge. Would it be okay if I could send you a pm?