The ejecta of thermally-pulsating AGB stars largely control the chemical evolution of galaxies. Yet, both, the mass-loss process and the gas chemical composition remain poorly understood. We present maps of the extended 12CO and 13CO emission in IRC+10216, the envelope of CW Leo, the high mass loss star the closest to the Sun. IRC+10216 is nearly spherical and expands radially with a velocity of 14.5 km/s. The observations, made with the IRAM 30-m telescope, have a sensibility, calibration, and angular resolution far higher than previous studies. The angular resolution is 11", which corresponds to an expansion time of 500 yr. The CO emission consists of a centrally peaked pedestal and a series of bright, nearly spherical shells. It peaks on CW Leo and remains relatively strong up to 180". Further out it becomes very weak and vanishes as CO gets photodissociated. The CO maps allow to trace the mass loss history in the last 8000 yr. The bright CO shells denote overdense regions, which indicate that the mass loss process is highly variable on timescales of hundreds of years. The new data, however, infirm previous claims of a strong decrease of the average mass loss in the last few thousand years. The overdense shells are not perfectly concentric and extend farther to the N-NW. The typical shell separation is 800-1000 yr in the middle of the envelope, but seems to increase outwards. The shell-intershell brightness contrast is $\geq$ 3. All those key features can be accounted for if CW Leo has a companion star with a period of $\sim$ 800 yr that increases the mass loss rate when it comes close to periastron. Higher angular resolution observations are needed to fully resolve the dense shells and measure the density contrast. The latter plays an essential role for our understanding of the envelope chemistry.

Accepted for publication in A&A. Text edited with respect to previous version