Your config.log shows that your system lacks the Qt development components necessary for building the octave-4.0 GUI:
configure:72095: checking for QT
configure:72103: $PKG_CONFIG --exists --print-errors "$QT_MODULES"
Package QtOpenGL was not found in the pkg-config search path.
Perhaps you should add the directory containing `QtOpenGL.pc'
to the PKG_CONFIG_PATH environment variable
No package 'QtOpenGL' found
configure:72106: $? = 1
configure:72121: $PKG_CONFIG --exists --print-errors "$QT_MODULES"
Package QtOpenGL was not found in the pkg-config search path.
Perhaps you should add the directory containing `QtOpenGL.pc'
to the PKG_CONFIG_PATH environment variable
No package 'QtOpenGL' found
configure:72124: $? = 1
No package 'QtOpenGL' found
configure:72152: result: no
configure:73317: WARNING: Qt libraries not found -- disabling GUI
You will need to install at least the Qt toolkit dependencies noted in the INSTALL.OCTAVE file that ships with the octave-4.0.0 source:
Qt
GUI and utility libraries (). Qt is required for building the GUI.
It is a large framework, but the only components required are the
GUI, core, and network modules.
The specific Ubuntu packages are libqtgui4 libqtcore4 and libqt4-network however unless disk space is severely limited you may wish to install the comprehensive libqt4-dev package instead
sudo apt-get install libqt4-dev
Although it's targeted at Debian rather than Ubuntu, you may find this additional resource helpful Octave for Debian systems: Compiling from source - The right way.