A matrix $Φ\in \mathbb{R}^{Q \times N}$ satisfies the restricted isometry property if $\|Φx\|_2^2$ is approximately equal to $\|x\|_2^2$ for all $k$-sparse vectors $x$. We give a construction of RIP matrices with the optimal $Q = O(k \log(N/k))$ rows using $O(k\log(N/k)\log(k))$ bits of randomness. The main technical ingredient is an extension of the Hanson-Wright inequality to $ε$-biased distributions.