In futuristic Startrek like scenarios you could in principle transmit all the information about the DNA and atoms that make up your body to a distance location and effectively a copy of you could be transmitted at the speed of light (ignoring the time to reconstruct your body) but you would not end up with time travel in the sense of travelling backwards in time.
Having rest mass prevents you from travelling exactly at the speed of light. Even if there was some hypthetical method such as the one I mentioned above that allows you to travel at the speed of light you would stillnot be able to travel backwards in time. To travel backwards in time you have to travel faster than the speed of light and particles with rest mass and light with zero rest mass can not exceed the speed of light. In theory a particle with imaginary rest mass can travel faster than light (eg the hypothetical tachyons) but these particles are unable to slow down to the speed of light or less.
What does it mean to have imaginary mass? A particle with imaginary mass can not interact with normal matter and it is very likely that it imposssible to detect tachyons using equipment made of normal matter. In theory there could be a whole universe of tachyonic matter superimposed on our universe but the tachyons would be unable to detect us (just as we can not detect them) and the tachyons would theorise that in principle there is matter that travels slower than light but those slow particles are undetectable and only theoretical (although we know we exist!). In other words to a tachyon we are made of imaginary mass.