A major goal of CMB experiments is to obtain highly sensitive CMB maps in order to extract Spherical Harmonic Power Spectrum (SHPS) and cosmological parameters with unprecedented accuracy. We present a new map-making code (Mirage), based on a two-phase iterative algorithm, involving low frequency drift treatment, Butterworth high-pass filtering and conjugate gradient method. This work was strongly motivated by Archeops CMB experiment data analysis. We believe that Archeops was a good test bench for the future Planck Surveyor data analysis, and Mirage was designed in order to be used for Planck data processing with minimal work. A strong feature of Mirage is that it handles experimental problems in data, such as holes in data stream, bright sources, and galaxy side effects, without jeopardising speed. The other advantage is its processing speed, allowing to run Monte Carlo simulations of Archeops data processing on a single processor workstation overnight. Algorithms are explained. Systematic effects on SHPS are investigated on various simulated data, including typical Archeops observational systematics.