Answer
It is possible to make a trip to a place farther than 70 light-years from Earth.
Work Step by Step
The ship can travel an arbitrary distance away from Earth if it reaches a high enough speed. To the Earth observer, the rocket's clock runs very slowly, and the rocket is traveling at nearly the speed of light.
For example, suppose the rocket is traveling fast enough that time appears to pass at only 1/10 of the Earth observer's rate, i.e., the time dilation factor is 10.
The rocket will travel 700 light years, while 70 years elapses for the person aboard the rocket.
