The parity check matrix has been changed to the following form (only new row combinations, but no permutations of the columns):
|   0 0 1 1   1 1 0 0   | |
H' |
|   1 1 0 0   0 0 1 1   | |
|   0 0 0 1   0 1 1 1   | |
This yields the following realization: