Move the declaration of the random number generator out of the loop.
The random number generation starts from a seed value. If the same seed is used repeatedly, the same series of numbers is generated. One way to produce different sequences is to make the seed value time-dependent, thereby producing a different series with each new instance of Random. By default, the parameterless constructor of the Random class uses the system clock to generate its seed value, ...
Source
By having the declaration in the loop you are effectively calling the constructor with the same value over and over again - hence you are getting the same numbers out.
So your code should become:
Random r = new Random();
for ...
string += r.Next(4);