Midrasch zu Schemot 9:31

4) as it is written (Vayikra 23:14): "And bread, and kali, and karmel you shall not eat until this self-same day, until you have brought the offering of your G d." "And if you offer a meal-offering of bikkurim to the L–rd": This is the meal-offering of the omer. From which (grain) does it come? From barley. — But perhaps it comes from wheat! R. Eliezer says (to negate this): It is written here (Vayikra 2:14): "aviv" (grain in the ear), and also in respect to Egypt (Shemoth 9:41). Just as "aviv" in respect to Egypt is barley, so, "aviv" here. R. Akiva says: It is written that the congregation is to bring bikkurim (the omer) on Pesach and that the congregation is to bring bikkurim (the two loaves) on Atzereth (Shavuoth). Just as we find that of that kind (of grain [i.e., wheat]) of which the individual brings his obligatory offering, the congregation brings its obligatory offering (the two loaves) on Atzereth — so, of that kind (i.e., barley), of which the individual brings his obligatory offering (the meal-offering of rancor of the sotah), the congregation is to bring its bikkurim (the omer) on Pesach. From which kind does the individual bring his obligatory offering? From barley. The congregation, too, is to bring its obligatory offering only from barley. An alternate derivation: If you say (that he brings it) of wheat, then the two loaves (which are of wheat) could not be (called) "bikkurim" (first fruits).