"has reached heights" is correct and usable in written English.
You could use it to describe a person or thing that has achieved success or a high level of accomplishment. For example, "She has reached heights of success that few could ever dream of."
"The purple fever has reached heights I've never seen before".
In Minnesota, helped by the rainiest April on record, the Mississippi River has reached heights not seen since the 1960s.
But the overall winner has unquestionably been the president, who has reached heights of power that the framers would scarcely have imagined.
The Supreme Court has tilted the playing field in favor of those who have benefitted most from rising inequality, giving the richest Americans a new tool to control the political process at a moment when their economic power has reached heights unequaled since 1929.
Since 1991, when Yeltsin dissolved the Soviet Union and post-Communist Russia was born, the country's onion domes have been regilded, luxury dachas have sprung up like mushrooms after a rain, and prosperity (for some Russians, at least) has reached heights not seen since Peter the Great and Catherine the Great built their fairy-tale palaces near the Neva River in the 18th century.
In a land where self-gratification has reached heights never dreamed of in ancient Rome, where self-esteem is more important than being able to read, and where self-help requires no more effort than putting on a cassette, the myth of quantum consciousness is just what the shrink ordered.
He added, "We've reached heights under Mayor Bloomberg; I want to make it even better, and reach new heights".
As it turned out, far from Britain being flooded with cheap wheat, within weeks of the abolition the price of grain had reached heights rarely seen before.
This abandonment of the working class by Labour, and the deep contempt that the Conservatives have for us, have had a devastating effect, the levels of inequality have reached heights not seen since the 1930s.
Twitter closed at $18.63 per share on Thursday, the day before the rumors started; by the time the bell rang on Monday afternoon, the stock had reached heights of $23.37, up further than the stock has been since January.
On the other hand, the popular arts have reached heights of creative brilliance and mass engagement that leave much of Britain's high culture looking stilted, lame and at times wilfully obscurantist.
