General aviation instructor pilot reported an early turn during a night departure with a student during a training flight; resulting in a departure heading procedure deviation and overflight of the ramp at about 75 feet.. The instructor returned to the departure procedure and continued the flight.

Narrative

In an attempt to adhere to the SNA departure noise abatement procedure departing Runway 20L; I failed to recognize my student had turned too far to the left and too early after departure; overflying Taxiway A and multiple parked aircraft on the south ramp at an altitude as low as what I judged to be 75 feet. Knowing we had turned too early for a safe departure; I instructed my student to continue on a more corrective heading to the right; and in doing so we violated the noise abatement procedure which requires a turn before the highway 73. Knowing I got behind the plane I asked Tower if I was cleared for crosswind; which I was then cleared for and I instructed my student to do so. Because I recognized the turn too late; I got distracted and when Tower told me radar contact after my crosswind turn and requested my altitude; I responded with requested cruising altitude instead of actual altitude; after which Tower requested me to explicitly state my actual altitude; which I responded with 900ft. While I did review the chart supplement; relevant county published website documents for the procedure; and reviewed the procedure with my student on the ground before takeoff from our home airport; I recognize my lack of familiarity with the area; compounded by the lack of visual references of nighttime contributed to this chain of unsafe events and violation of noise abatement procedures.