Generate (not so)random string with particular string occurences

I have a requirement where I have the alphabet 'ACGT' and I need to create a string of around 20,000 characters. This string should contain 100+ probabilities of the pattern "CCGT". Most of the time the generated string contains it around 20-30 instances.

    int N = 20000;
    std::vector<std::string> vecStr;
    std::string alphabet("ACGT");
    std::string str;
    str.reserve(N);
    for (int index = 0; index < N; index++)
    {
        str += alphabet[rand() % (alphabet.length())];
    }

How do I tweak the code so that the pattern would appear more often?

Thank you.