Unable to type in Greek using iBus but can type Japaneese and English as well

According to an answer to my askubuntu question I managed to switch from xkb input into iBus one. I have installed via iBus the English, Greek and Japaneese (Anthy) keyboard language.

But when I type in Greek no Greek letters are shown, but I can easily type Japanese via Anthy and English as well.

The iBus setting are as the following screenshot shows:

Ibus Settings

The command dconf list /org/mate/desktop/peripherals/keyboard/ shows the following result:

numlock-state

Whilst the /etc/default/keyboard has the following settings:

# KEYBOARD CONFIGURATION FILE

# Consult the keyboard(5) manual page.

XKBMODEL="pc105"
XKBLAYOUT="us"
XKBVARIANT=""
XKBOPTIONS=""

BACKSPACE="guess"

Event changing into the following settings has no effect whatsoever:

# KEYBOARD CONFIGURATION FILE

# Consult the keyboard(5) manual page.

XKBMODEL="pc105"
XKBLAYOUT="us,gr"
XKBVARIANT=""
XKBOPTIONS=""

BACKSPACE="guess"

So how I can enable iBus to manage the Greek layout as well? I need iBus because I find it convenient using the Anthy Japanese input instead of the mozc one.

For your problem @pc_magas you can have a look upon this askubuntu answer. It is for the EXACLTY same problem you have.