Small aircraft pilot reported turning too early on an IFR departure with a high rate of descent and unknowingly cleared the airport hangars by 150 ft.

Narrative

Ferry flight form BJC to ZZZ1 for multi-engine check ride. I was flying left seat with flight school instructor in the right seat; CFI only with multi-engine rating. Fog with 0.25 visibility up to 300 ft. over airfield. IFR flight plan filed requiring DENVER2 Departure off 30R with initial heading of 350. Tower requested a call on takeoff because they were unable to see us on the airfield. Takeoff was briefed but I failed to detail how we would mitigate the risks involved with an IFR takeoff. It had been a month since I had done any instrument flying but I was still current. At rotation speed I was on an instrument scan pitching for best rate of climb. Halfway down the runway; after we lifted off; I dropped a proper instrument scan and started an early turn from 300 to 350. This resulted in a 500 ft./min rate of descent along with a turn toward hangars on the east side of the runway. The CFI pointed out my error in turning early but I was confused and kept my turn in. He correctly turned his attention to our 500 ft./min rate of descent; and pulled back on the yoke arresting our descent. After looking at ForeFlight we cleared the hangars by 150 ft. The mistake of not staying on runway heading resulted in the breakdown of my instrument scan on climb-out and could have resulted in controlled flight into terrain.