Rate of Koetter-Kschischang Codes

Question

I'm studying this article on coding theory. Here $W$ denotes a $N$-dimensional vector space over $\mathbb{F}_q$. A code $C$ then consists of code words $V\in C$, where $V\subseteq W$ is a subspace of $W$. Let $l$ denote the maximum dimension of a codeword $V$, i.e. $l=\max_{V\in C} \dim (V)$. Now the article defines the rate of this code as $$ R=\frac{\log_q|C|}{Nl}$$ but I'm not sure why this is a natural definition. Clearly transmitting a codeword requires transmitting $N\cdot l$ symbols in $\mathbb{F}_q$. But shouldn't this be done for every codeword? And I guess $|C|$ can be thought of as the total number of information symbols, so why do we take $q$-logarithm?