You really need to sit down with an elder law attorney to get an answer to such a specific question. The answer may be as easy as transferring the mineral rights into the name of the healthy spouse or you might be advised to transfer them to a trust in case you both need care.
Only a local elder law attorney who knows local practices and can look at this asset in the context your other assets and income will be able to advise you.
Find a qualified elder law attorney near you.
For more on Medicaid's asset transfer rules, check out this article, or learn more about how Medicaid treats income here.
You may also want to read this piece on Medicaid's protections for the healthy spouse.