What is the strength and attack vectors of this simple scheme?
Short answer: Sorry, no, unfortunately your concept is neither a secure, practical nor efficient crypto scheme.

Slightly longer answer: To illustrate the impractically of your scheme, let's assume you are sending a completely random bit string $S$ of length $B$. In such case, in order to preserve perfect secrecy, you will at least have to send a list $L$ containing all possible values $[0..2^B)$ in random order, except for $S$ which is fixed at position $M$, where $M$ is the secret key you share with the recipient. 

Now, if $M$ is selected completely at random from all possible values, it will also be a random element from $[0..2^B)$ and consequently be exactly as long, and contain as much entropy as, the message $S$ you want to sent. 

The cipher text $L$ on the other hand, will be exponentially longer than the plain text message $S$. This is bad, because it means that your effort of sending the message securely, will be exactly as great as the effort you want your adversary to suffer trying to brute force guessing the key or the plain text.

Furthermore, if the plain text $S$ is not completely random, securely executing your scheme gets more complicated, but the conclusion doesn't change. If you maximize security, your effort of encoding and sending the plain text will be no less than the effort you want your adversary to suffer trying to break your scheme.