HDG TRACK DEV BY A B757 FLC DURING THE KODIX 2 DEP PROC FROM MDSD; FO.

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I COMPLETELY BOTCHED THE DEP OUT OF SDQ. GIVEN RWY HDG TO 3000 FT OFF RWY 17. WE HAD THE KODIX 2 DEPROGRAMMED AND I ASKED FOR LNAV AFTER TKOF. STARTED A L TURN PER THE SID INSTEAD OF RWY HDG. WHEN SDQ REALIZED WHAT WE HAD DONE; I THOUGHT I HEARD MAINTAIN PRESENT HDG AND 3000 FT. I REALIZED THAT THE HDG WE WERE ON WOULD TAKE US OVER THE PROHIBITED AREA AND TURNED N. WHEN THINGS SETTLED DOWN DEP SAID THAT WE HAD MISSED THE PROHIBITED AREDA BY 4 MI. IT WAS MY ERROR. WE HAD COPIED AND READ BACK RWY HDG AND 3000 FT TO 10 DME. NO PROB WITH COM UNTIL DEP SAW WE HAD TURNED AND GOT A LITTLE EXCITED. WHAT I THINK LULLED ME INTO THIS WAS THAT WE HAD INITIALLY PLANNED RWY 35 AS PER ATIS AND KODIX 2 AS PER FLT PLAN. WE CHANGED RWY IN FMC; BUT LEFT THE DEP. I HAD BRIEFED THAT I WOULD USE LNAV AFTER TKOF BEFORE WE WERE GIVEN RWY 17. I HAVE NO VALID EXCUSE FOR THIS. SEQ DEP WAS CONCERNED WITH A CONFLICT WITH A NAVY ACFT ALSO IN THEIR AIRSPACE. SUPPLEMENTAL INFO FROM ACN 564236: CREW BRIEFED AND PLANNED FOR THE KODIX DEP PROC OFF OF RWY 35; BASED ON OUR INITIAL FIX ENRTE AND THE ATIS INFO AT SDQ. ENRTE CLRNC WAS REQUESTED 15 MINS BEFORE PUSHBACK; BUT WAS NOT ISSUED UNTIL TAXI OUT. THE CLRNC DID NOT MENTION THE KODIX DEP; BUT DID TELL US TO EXPECT RWY 17 INSTEAD OF RWY 35. WE SHOULD HAVE FLOWN RWY HDG. DEP CTL WAS TALKING WITH A NAVY ACFT; SO WE DID NOT ESTABLISH COMS WITH THEM UNTIL WE WERE HDG N AND LEVEL AT 3000 FT. AS SOON AS WE ESTABLISHED HIS SURPRISE WITH OUR HDG; WE REALIZED WHAT HAD HAPPENED. THERE WAS A NAVY ACFT IN THE AREA WHOSE CLRNC HAD TO BE CHANGED BY THE CTLR TO AVOID A CONFLICT.