Both the sentences are correct and it seems the second one is better. The 'that clause' here acts as the object of 'means'. The meaning of the sentence is clear even without the presence of the conjunction 'that' and it has nothing extra to add to the meaning as well.
The inclusion or omission of 'that' is a matter of formal or informal style. We can often leave out the conjunction or relative pronoun 'that' in the informal style.
'That' cannot be dropped after certain verbs (e.g. reply,
telegraph, shout), and it is not dropped after nouns.
She shouted that she was busy.
NOT, She shouted she was busy.*
He disagreed with Copernicus' view that the earth went round the sun.
NOT, He disagreed with Copernicus' view the earth went round the sun.
But, we can usually leave out the relative pronoun that when it is the object in a relative clause.
Look! There are the people (that) we met in Brighton.
Do it the way (that) I showed you.
( Based on Michael Swan's PEU )