All binary codes of length up to 15 and dimension up to 6 are classified and their generator matrices are given in the following links. The format of the data is:  k n 2, where k is the dimension of the code, n its length and 2 means binary. Then the rows of the generator matrix of the code follows.

 

Codes of dimension 2

Codes of dimension 3

Codes of dimension 4

Codes of dimension 5

Codes of dimension 6