Use custom function

As commented you may create a function that if called with a custom colorname returns the hex color from the list.

import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns

# Wanted palette details
enmax_palette = ["#808282", "#C2CD23", "#918BC3"]
color_codes_wanted = ['grey', 'green', 'purple']

c = lambda x: enmax_palette[color_codes_wanted.index(x)]

x=np.random.randn(100)
g = sns.distplot(x, color=c("green"))

plt.show()

Use the C{n} notation.

It should be noted that all colors in seaborn are matplotlib colors. One option matplotlib provides is the so called C{n} notation (with n = 0..9). By specifying a string like "C1" you tell matplotlib to use the second color from the current color cycle. sns.set_palette sets the color cycle to your custom colors. So if you can remember their order in the cycle you can use this information and just specify "C1" for the second color.

import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns

# Wanted palette details
enmax_palette = ["#808282", "#C2CD23", "#918BC3"]

sns.set_palette(palette=enmax_palette)

x=np.random.randn(100)
g = sns.distplot(x, color="C1")

plt.show()

Manipulate the matplotlib color dictionary.

All named colors are stored in a dictionary you can access via

matplotlib.colors.get_named_colors_mapping()

You may update this dictionary with your custom names and colors. Note that this will overwrite existing colors with the same name.

import numpy as np
import matplotlib.pyplot as plt
from matplotlib import colors as mcolors
import seaborn as sns

# Wanted palette details
enmax_palette = ["#808282", "#C2CD23", "#918BC3"]
color_codes_wanted = ['grey', 'green', 'purple']
cdict = dict(zip(color_codes_wanted, [mcolors.to_rgba(c) for c in enmax_palette]))

mcolors.get_named_colors_mapping().update(cdict)
x=np.random.randn(100)
g = sns.distplot(x, color="green")

plt.show()

All codes shown here will produce the same plot in "the company's green" color:

If by "6 digit code" you mean a hex code, you can also do:

pal = sns.color_palette(...)
pal.as_hex()