A uniform set with fewer than expected arithmetic progressions of length 4

An example is presented of a subset $A$ of ${\mathbb{Z}}_N$ of density $\alpha$ such that the largest non-trivial Fourier coefficient of the characteristic function of $A$ is very small, but the probability that a random arithmetic progression (mod $N$) of length 4 lies in $A$ is significantly smaller than ${\alpha }^4$.