Below $T\ensuremath{\approx}150 \mathrm{K},$ the spin arrangement in the chain arrays of ${\mathrm{Sr}}_{14}{\mathrm{C}}_{24}{\mathrm{O}}_{41}$ is shown to develop in two dimensions. Both the correlations and the dispersion of the observed elementary excitations agree well with a model of interacting antiferromagnetic dimers. Along the chains, the intra- and interdimer distances are equal to 2 and $\ensuremath{\approx}3$ times the distance (c) between neighboring Cu ions. While the intradimer coupling is $J\ensuremath{\approx}10$ meV, the interdimer couplings along and between the chains are of comparable strength, ${J}_{\ensuremath{\Vert}}\ensuremath{\approx}\ensuremath{-}1.1 \mathrm{meV}$ and ${J}_{\ensuremath{\perp}}\ensuremath{\approx}1.7 \mathrm{meV},$ respectively. This remarkable two-dimensional (2D) arrangement satisfies the formal Cu valence of the undoped compound. Our data suggest also that it is associated with a relative sliding of one chain with respect to the next one, which, as T decreases, develops in the chain direction. A qualitative analysis shows that nearest interdimer spin correlations are ferromagnetic, which, in such a 2D structure, could well result from frustration effects.