Possible Dimensions of Linear Codes with length $n$ over $GF(q)$

Question

We need to calculate the number of linear codes(note not codewords) with length $n$ over $GF(q)$ , the number of linear codes with dimension k is $$\frac{\prod_{i=0}^{k-1}(q^{n} - q^i)}{\prod_{i=0}^{k-1}(q^{k} - q^i)}$$,let's assume $n=20, q=5$ but in our case dimension is not specified so we need to sum over all the possible dimension , for linear codes the possible dimension are $d=[1,n]$ (correct me if I am wrong) where $n = 20$ in our case , so the formula will be $$\sum_{k=1}^{20}\frac{\prod_{i=0}^{k-1}(5^{20} - 5^i)}{\prod_{i=0}^{k-1}(5^{k} - 5^i)}$$ which gives about $1.456*10^{70}$, I could not find any resources about the possible dimensions of linear codes, could you please give some resources specifically investigating it for linear codes, and hamming codes.