Download the driver package from here:

http://support.epson.net/linux/en/iscan.php?model=gt-x770&version=2.30.4

wget "https://download2.ebz.epson.net/iscan/plugin/gt-x770/deb/x64/iscan-gt-x770-bundle-2.30.4.x64.deb.tar.gz"
tar -xvzf iscan-gt-x770-bundle-2.30.4.x64.deb.tar.gz
cd iscan-gt-x770-bundle-2.30.4.x64.deb


# As libsane was renamed to libsane1, the dependencies of the deb packages need to get adjusted:
cd core
mkdir epson-sane
dpkg-deb -R iscan_2.30.4-2_amd64.deb epson-sane/
sed -i "s/libsane /libsane1/" epson-sane/DEBIAN/control
dpkg-deb -b epson-sane/ epson-sane-modified.deb
mv epson-sane-modified.deb iscan_2.30.4-2_amd64.deb
rm -rf epson-sane
cd ..

cd data
mkdir epson-sane
dpkg-deb -R iscan-data_1.39.2-1_all.deb epson-sane/
sed -i "s/libsane /libsane1/" epson-sane/DEBIAN/control
dpkg-deb -b epson-sane/ epson-sane-modified.deb
mv epson-sane-modified.deb iscan-data_1.39.2-1_all.deb 
rm -rf epson-sane
cd ..

sudo ./install.sh

The following may be required on Ubuntu based system (rather than Debian) to move the scanner drivers in the correct directory

sudo cp /usr/lib/sane/* /usr/lib/x86_64-linux-gnu/sane/
sudo cp /usr/lib/x86_64-linux-gnu/sane/* /usr/lib/sane/

iscan needs to be started as root:

sudo iscan

To let users access the device which changes bus and device each time it is started, add a udev rule based on the manufacturer and device code. It's the ID 04b8:0130 but where 04b8 is EPSON and 0130 the particular model.

lsusb

Also add yourself to the saned and scanner groups (replace username with the actual username):

sudo adduser username saned
sudo adduser username scanner 

Now add the following to /etc/udev/rules.d/80-scanner.rules

80-scanner.rules

# change device EPSON owner group
ATTRS{manufacturer}=="EPSON", DRIVERS=="usb", SUBSYSTEMS=="usb", ATTRS{idVendor}=="04b8", ATTRS{idProduct}=="0130", GROUP="scanner"

Reload udev rules:

sudo udevadm control --reload

And test the rules replacing the bus and device number from lsusb output. This should print group id 0 in the first line, then the group id of the scanner group in the second line.

sudo udevadm test $(udevadm info -q path -n /dev/bus/usb/<bus>/<device>) 2>&1 | grep -i group --color

Disconnect the scanner and reconnect it, then try using iscan or other scanning applications.