An utmost importance is not natural English. It would not surprise me if the author of your example is not a native speaker.
The issue of English having count nouns and mass (or non-count) nouns is a poor way to talk about nouns in English.
A better way is to say that nouns can be used as count nouns, non-count nouns, or both.
Some nouns in English can be used as both count nouns and non-count nouns. Let's look at freedom.
It can be used as a count noun:
The USA guarantees its citizens many freedoms that other countries do not.
It can also be used as a non-count or mass noun:
Freedom, just like life and liberty, is highly-cherished by most citizens.
Ultimately, what decides whether a noun can be used as count, non-count, or both is the community of English speakers. Some nouns used only as mass nouns today were once used as both.
But importance is used only as a non-count noun in today's English.
As for your actual question:
You cannot use the indefinite article with a singular noun used as a non-count noun.
The following is ungrammatical:
An importance has come to mind today.
You can say:
Waiter, I'll have a cappuccino to drink.
because a cappuccino is conceptualized as a serving of cappuccino.
You can say:
This coffee is a coffee that is out of this world.
because a coffee is conceptualized as a type of coffee.
You can use the definite article with singular or plural count and non-count nouns.
Best Answer
System is countable.
Compare:
It could it be that in the name of the first article, the indefinite article a was dropped due to style considerations, because this looks more correct:
I cannot think of a sentence where system would be uncountable.