  In this contribution, we completely and explicitly characterize Young
measures generated by gradients of quasiconformal maps in the plane. By doing
so, we generalize the results of Astala and Faraco \cite{AstalaFaraco} who
provided a similar result for quasiregular maps and Bene\v{s}ov\'a and
Kru\v{z}\'ik \cite{bbmk2013} who characterized Young measures generated by
gradients of bi-Lipschitz maps. Our results are motivated by non-linear
elasticity where injectivity of the functions in the generating sequence is
essential in order to assure non-interpenetration of matter.
