  We present results for the $I=2$ $\pi\pi$ scattering length using $N_f=2+1+1$
twisted mass lattice QCD for three values of the lattice spacing and a range of
pion mass values. Due to the use of Laplacian Heaviside smearing our
statistical errors are reduced compared to previous lattice studies. A detailed
investigation of systematic effects such as discretisation effects, volume
effects, and pollution of excited and thermal states is performed. After
extrapolation to the physical point using chiral perturbation theory at NLO we
obtain $M_\pi a_0=-0.0442(2)_\mathrm{stat}(^{+4}_{-0})_\mathrm{sys}$.
