Is this the correct way to generate a set of Gold codes:
Take a preferred pair of M sequence polynomials and load each one of them into a separate LFSR. The serial bit streams that are generated from this process are combined using an exclusive or gate; the result is a gold code bit stream.
Sort of. One does not "load" a preferred pair of m-sequences into separate LFSRs; the coefficients of the m-sequence specify the feedback connections of the LFSR. What is loaded into each LFSR is the seed which determines which Gold sequence (sometimes called a Gold code) is generated. Gold sequences are periodic and to avoid getting the same Gold sequence but with a different starting point (a strict no-no for asynchronous CDMA) when using assigning different seeds for different users, it is best to assign the same (nonzero) seed for one LFSR to all users, and to assign different (nonzero) seeds for the other LFSR to different users.
Code length of 64 gives a family size of 6. Does a family size of 6 mean that I have to generate 6 codes to divide 6 users in a channel using the method I described above with a different seed every time?
Er, no, Gold sequences have periods (or lengths) of the form $2^n-1$ and so you likely meant $63$, not $64$. There are $65$ Gold sequences (not $6$ as you think) of period $63$ consisting $63$ sequences generated by nonzero seeds in each LFSR, and the two m-sequences which are generated when one LFSR is loaded with a zero seed and other has a nonzero seed. Each of these $65$ sequences of length or period has $63$ different cyclic shifts giving a total of
$$65\times 63 = (2^6+1)\times (2^6-1) = 2^{12}-1$$
"different" nonzero outputs that might be observed. As Dan Boschen's answer (after replacing $10$ with $6$ mutatis mutandis) points out, Gold sequences of period $63$ can be generated with a $12$-bit LFSR whose feedback taps correspond to the product of the two preferred polynomials, and the $2^{12}-1$ "different outputs" of this $12$-bit LFSR can be grouped into sets of $63$ cyclically-equivalent Gold codes.
For more than you probably want to know, I refer you to the paper D.V. Sarwate and M.B. Pursley, "Cross-correlation properties of pseudorandom and related sequences," Proc. IEEE, vol.68, pp.593-619, May 1980. It includes a detailed discussion of the Gold sequences as well as the small sets and large sets of Kasami sequences.