I managed to make it up and running. I did a stupid thing: ctrl_interface is not path to interface so here is the working config...
Code:
ctrl_interface=/var/run/wpa_supplicant
ctrl_interface_group=root
ap_scan=0
network={
key_mgmt=IEEE8021X
eap=PEAP
pairwise=CCMP
identity="<>"
password="<>"
phase2="auth=MSCHAPV2"
}
I flashed OpenWrt and it even works there.