Non-polynomial Turing Machine

Hi, can anyone help with the following?

Given the Language $\displaystyle L\ = \{\sigma1^{3k}}\in \{0,1\}^* \mid \sigma\ codes\ a\ Turing\ Machine\ M\ which\ on\ insert\ \sigma1^{3k}}\ halts\ within\ at\ most\ 2^k\ steps\ without\ accepting\ \} $

Show that $\displaystyle L \notin P $ and find a function $\displaystyle T(n) $ such that $\displaystyle L \in Time(T(n)) $

This the first time I have been asked to show a language is not in some class, and I'm quite stumped.