It does make sense—just not the sense you’re trying to express.
While to beat can mean many things, the context here sounds very much like some kind of competitive activity, which means the definition of to beat that most readers will have is
4 a : OVERCOME, DEFEAT
which does roughly line up with what you mean to express. However, in this context, when you “overcome” his distance, we understand that to mean that your distance is greater than his. For example, if the competition were the long jump, you would “beat the distance” he had set when you jump an even greater distance.
It would not mean you had overcome the distance by which he was ahead of you, e.g. in a race. In a race, “to beat the distance” has no clear meaning and would leave most of the audience confused. A more typical phrase for accomplishing that could be “to close the gap,” or “to make up time.”