Should he take zakaah to build himself a house?

Praise be to Allah.

Accommodation is one of the basic needs which no one can do without. This need may be met by buying a house or building it or renting it. There is nothing wrong with giving zakaah to someone who owns land but cannot afford to build on it. He comes under the general heading of poor and needy who are among those to whom zakaah may be given, as Allaah says (interpretation of the meaning): 

“As-Sadaqaat (here it means Zakaah) are only for the Fuqaraa’ (poor), and Al‑Masaakeen (the poor) and those employed to collect (the funds); and to attract the hearts of those who have been inclined (towards Islam); and to free the captives; and for those in debt; and for Allaah’s Cause (i.e. for Mujaahidoon — those fighting in a holy battle), and for the wayfarer (a traveller who is cut off from everything); a duty imposed by Allaah. And Allaah is All-Knower, All-Wise”

[al-Tawbah 9:60]

It says in Badaa’i’ al-Sanaa’i’ (2/48): There is nothing wrong with giving zakaah to one who has a house, furnishings, a servant, a horse, a weapon, clothing and books of knowledge, if he is one of the people’s of knowledge, but if he has more than that, to a value of two hundred dirhams, it is haraam for him to take zakaah, because these things are necessities of life that a person cannot do without. End quote. 

If this applies to one who has accommodation and furnishings but does not have enough to live on, then one who does not have these basic necessities is even more entitled to zakaah. 

Abu ‘Ubayd al-Qaasim ibn Salaam said in his book (p. 750) that if a man sees that the family of a righteous Muslim are poor and needy, and he is wealthy, but they do not have a house to give them shelter, and he buys a house with the zakaah of his wealth to protect them from the cold of winter and the heat of the sun, and gives that from the zakaah of his wealth, then he will be doing an obligatory duty and he will be doing a good deed. End quote. 

See: Ahbaath Fiqhiyyah fi Qadaaya al-Zakaah al-Mu’aasirah (1/369). 

 If a poor person does not have accommodation or furnishings, it is permissible to buy what he needs from zakaah funds. End quote. 

Based on this, there is nothing wrong with your accepting help from your colleagues on the basis that this is zakaah. 

And Allaah knows best.