What are some things that validate the statements that Wudi "took China to new heights" and that he "strenghtened the government and economy?"
Han Wudi was the Emperor of China from 140 to 87 BCE. His reign was a time of great expansion of the empire (his name meant "Martial Emperor) and also of reforms that improved the country.
Wudi took China to new heights by conquering a great deal of territory and adding it to the empire. His armies moved south, taking much of what is now Southeast China along with parts of what is now Vietnam. They also took Korea. In the other direction, they pushed the Xiongnu back behind the Great Wall.
In domestic affairs, Wudi implemented important reforms. He instituted the system of having people take exams in order to become government officials. He set up a university for training people to take those exams. He also created programs for controlling floods and sponsored caravans that traded with the West. All of these could be seen as examples of strengthening the government and the economy.