And here's a function to plot a compact calendar with matplotlib:

import calendar
import numpy as np
from matplotlib.patches import Rectangle
import matplotlib.pyplot as plt

def plot_calendar(days, months):
    plt.figure(figsize=(9, 3))
    # non days are grayed
    ax = plt.gca().axes
    ax.add_patch(Rectangle((29, 2), width=.8, height=.8, 
                           color='gray', alpha=.3))
    ax.add_patch(Rectangle((30, 2), width=.8, height=.8,
                           color='gray', alpha=.5))
    ax.add_patch(Rectangle((31, 2), width=.8, height=.8,
                           color='gray', alpha=.5))
    ax.add_patch(Rectangle((31, 4), width=.8, height=.8,
                           color='gray', alpha=.5))
    ax.add_patch(Rectangle((31, 6), width=.8, height=.8,
                           color='gray', alpha=.5))
    ax.add_patch(Rectangle((31, 9), width=.8, height=.8,
                           color='gray', alpha=.5))
    ax.add_patch(Rectangle((31, 11), width=.8, height=.8,
                           color='gray', alpha=.5))
    for d, m in zip(days, months):
        ax.add_patch(Rectangle((d, m), 
                               width=.8, height=.8, color='C0'))
    plt.yticks(np.arange(1, 13)+.5, list(calendar.month_abbr)[1:])
    plt.xticks(np.arange(1,32)+.5, np.arange(1,32))
    plt.xlim(1, 32)
    plt.ylim(1, 13)
    plt.gca().invert_yaxis()
    # remove borders and ticks
    for spine in plt.gca().spines.values():
        spine.set_visible(False)
    plt.tick_params(top=False, bottom=False, left=False, right=False)
    plt.show()

You can use it to highlight the days with full moon in 2018:

full_moon_day = [2, 31, 2, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22]
full_moon_month = [1, 1, 3, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]
plot_calendar(full_moon_day, full_moon_month)

Or just highlight all the weekends:

from datetime import datetime, timedelta

def get_weekends(year):
    weekend_day = []
    weekend_month = [] 
    start = datetime(year, 1, 1)
    for i in range(365):
        day_of_the_year = start + timedelta(days=i)
        if day_of_the_year.weekday() > 4:
            weekend_day.append(day_of_the_year.day)
            weekend_month.append(day_of_the_year.month)
    return weekend_day, weekend_month

weekend_day, weekend_month = get_weekends(2018)
plot_calendar(weekend_day, weekend_month)