Gulfstream GIV pilot reported failure of the Flight Guidance Computer during departure in IMC resulted in return to departure airport.

Narrative

During a right-seat takeoff from Runway XX; following the ZZZZZ departure protocol; the aircraft encountered a severe systems malfunction. At approximately 1400 feet altitude; the Flight Guidance Computer (FGC) 1-2 failed; resulting in the loss of both the Flight Director Control Unit and the display units.The incident occurred under Instrument Meteorological Conditions (IMC) with prevalent icing conditions; significantly impairing visibility and navigational capabilities.As the Pilot in Command; I observed an inability to reduce power effectively; despite attempts to do so; the aircraft continued to gain speed. This unusual behavior was noted by ZZZ Departure Control; who inquired if [priority handling] was necessary due to the increasing speed and altitude. Acknowledging the severity of the situation; I [requested priority]. Following the [request]; ZZZ Departure provided vectors for an approach to Runway XY. I instructed the First Officer to run the approach and pre-landing checklist to ensure all safety protocols were followed.Upon approach to Runway XY; the IFR conditions rendered the runway invisible. A go-around procedure was initiated. During the ascent; we gained visual contact with the runway environment.Seizing the moment; I requested permission from ZZZ Tower to perform a 360-degree maneuver for a safer approach and landing on Runway XX. The tower approved this request.The aircraft successfully executed the maneuver and safely landed on Runway XX. The dynamic response to the unfolding events by the flight crew was instrumental in the safe resolution of this event.