The block code $C\subseteq GF(2) ^6$ consists of all binary sequences of length 6 with hamming weight $w = 4$. The rate of a block code is defined as the ratio between its message length and its block length:
$$R=k/n$$
How do I know what is k in my code? n=6
You have $\binom{6}{4}=15$ codewords and a nonlinear code since sum of two codewords need not be a codeword. Thus the rate of your code is $$\log_2 15/6$$ but the dimension is undefined in the usual sense.
Linear codes, being vector subspaces, have well defined dimensions, which are integers.