  The shifts in the four-body recombination peaks, due to an effective range
correction to the zero-range model close to the unitary limit, are obtained and
used to extract the corresponding effective range of a given atomic system. The
approach is applied to an ultracold gas of cesium atoms close to broad Feshbach
resonances, where deviations of experimental values from universal model
predictions are associated to effective range corrections. The effective range
correction is extracted, with a weighted average given by 3.9$\pm 0.8 R_{vdW}$,
where $R_{vdW}$ is the van der Waals length scale; which is consistent with the
van der Waals potential tail for the $Cs_2$ system. The method can be generally
applied to other cold atom experimental setups to determine the contribution of
the effective range to the tetramer dissociation position.
