Random numbers with Gaussian distribution

Hi, i try to program a white noise generator with gaussian distribution. When i first used the rand() function i connected the 12-Bit DA-converter to a speaker.
A periodic timer interrupt (about 400kHz) gets a rand number and puts it to the DA-converter.

I expected white noise, but wasn't satiesfied, i could hear a hum inside the white noise. The random numbers seemed to have some periodic pattern with a high repeat rate inside. I think with a spectrum-analyzer there would be some extra lines inside the spectrum. Now i wrote my own rand() function.

//***************************************************************************
int my_rand(int init_rand)
{
        static unsigned int Z;
        if (init_rand) Z = init_rand;

        if (Z & 0x80000000)
        {
                Z<<=1;
                Z^=0x04C11DB7;//i saw it in a dream ;-)
        }
        else
        {
                Z<<=1;
        }
        return Z;
}
//***************************************************************************

After once beeing initialised with a value not zero it sounds great.

But is it mathematical correct?

After how many cycles does the initial value return?

Can i get a pseudo gaussian distribution with the following?

        Z = my_rand(0);
        K = ((Z>>11 ^ Z>>22) & 0x3FF)
           +((Z>>11 ^ Z    ) & 0x3FF)
           +((Z>>22 ^ Z>>5 ) & 0x3FF)
           +((Z     ^ Z>>17) & 0x3FF);

        DAC0DAT = K<<16;//the 12bit-ADuC7026-DA-converter

There must be a more elegant method to have gaussian distribution!

Thanks for advice.