Pilot reported that they did not fly the correct heading as assigned resulting in a CFTT/CFIT during departure from BOI airport.

Narrative

I departed BOI on an instrument flight plan from BOI to ZZZ1. The flight was a return home trip from an Angel Flight Mission from ZZZ2 to BOI that morning. I was flying with a pilot friend; a CFI. The flight plan I had filed provided for a direct routing BOI to ZZZ1. After engine start; I contacted Clearance Delivery and was cleared to depart BOI; Runway 10L; maintain runway heading for vectors to VALYY intersection; direct to ODYSY; and then as filed; maintain 16;000 FT; and expect FL260 in 10 minutes. Departure freq 119.6. Weather was severe clear. The VALYY and ODYSY intersection were specified and inserted by Clearance Delivery at BOI prior to takeoff. We were cleared to taxi to Runway 10L. As I was taxiing from the FBO to Runway 10L; my friend was programming the inserted instructions into the GTN750 flight plan that I had previously programmed. Approaching Runway 10L we were instructed to hold short for landing traffic. During the holding short period; two or three other small aircraft and a regional airliner or large corporate jet pulled up behind us also waiting for departures on Runway 10L; so I was concerned about holding up a parade of departures on Runway 10L and not 100% focused on the specific departure instructions I had been given. After takeoff and climbing to approximately 3;550 feet MSL; I turned left for direct to VALYY intersection and was handed off to Boise Departure. In less than a minute Departure notified me of a pending terrain issue and asked if I could climb VFR for terrain avoidance; which I did. Departure said I was cleared direct to VALYY upon reaching 8;000 FT MSL. Shortly thereafter; Departure gave me a contact number to call post-flight for a possible incident or violation. The remainder of the flight was uneventful. After landing at ZZZ1 I called the number I was given; discussed the incident briefly and was told that I would possibly receive a call for further discussion or action. In retrospect; I was focused on the two new intersections that were inserted when we were given the clearance and over looked the 'fly runway heading' portion of the clearance; which I had copied down and read back to Clearance Delivery. Clearly my mistake. Of note; my CFI pilot friend; sitting next to me; also did not realize we had diverted from the cleared routing. I think if the clearance had simply been to fly the Boise Three Departure; which is essentially a straight out departure for Runway 10L; for vectors to VALYY; then direct ODYSY; I probably would not have turned prematurely away from runway heading and toward VALYY. I would just be flying the departure; waiting for the clearance direct to VALYY.