That was a job. After soldering 736 components and approximately 160 wires, the 30 years old display is alive.

Some pictures of the back (please apologize the wire-mess) :

And the front :

And below the serial connection in action (115200 bauds, 5 frame per second, images taken around the mouse cursor of the computer) :

As you can see there is still some artifacts, especially on the screen bottom. I still have to adjust the cathode bias resistor value.

A funny fact is the screen is buzzing, adding a very old fashion touch to the retro style, in addition to remind you there is 360 volts in here. 

Next step: a convenient and safer case !