Air carrier pilot reported Tower issued a departure heading which resulted in flight towards terrain.

Narrative

Possible Lateral deviation; After 'line up and wait' on Runway 34 SXZ we were given 'clear for takeoff fly heading 010'. The original printed clearance was fly SIE9ZD so we were surprised slightly. I read back the clearance and emphasized the heading given; no response from Tower. We took off and at 1000 ft hit the heading select and rotated 010. The Tower then transferred us to departure. I again emphasized the heading we were given and read back the frequency; no comment from Tower. We checked on with departure and I again emphasized we were on a heading of 010. A Few seconds later and about 1500 ft departure queried us about a lateral deviation and gave us a terrain warning. I informed Departure that Tower had given us the heading but he seemed confused by this. I responded with clear of terrain in VMC and we were given a new heading with a left turn away from the parallel runway and any hills. Departure continued to ask about the deviation so we gave him all the information we had. Apparently he thought we were flying on the SIE9ZD. Cause: The Tower operator had a thick accent and broken English. The takeoff clearance wasn't verbalized clear enough. I should have reminded stopped and asked clarification before takeoff as it was hard to understand the Tower operator. Suggestions: Stop and ask when on the ground and something doesn't sound right.