How can I shelter myself from a Capital Gains Tax on the selling of my primary residence? Look to do a new construction build, but my debt to income is maxed.

Looking to secure a Land Loan and then due diligence to execute the construction loan.  I have equity in the house I currently own, but don't know if the timing will be right for selling my primary residence and closing on the construction loan.  Ofcourse, the least amount of money going back to the government is the end goal here.