Thank you for your answers.
I came to conclusion that I could drive the whole matrix (this one by the way) with only 2x74HC595.
In my head, the thing goes like:
Sequence 1-1: Row 1 - analogWrite() to RED1
Sequence 1-2: Row 1 - analogWrite() to GREEN1
Sequence 1-3: Row 1 - analogWrite() to BLUE1
...
Sequence 1-10: Row 1 - analogWrite() to RED4
Sequence 1-11: Row 1 - analogWrite() to GREEN4
Sequence 1-12: Row 1 - analogWrite() to BLUE4
Sequence 2-1: Row 2 - analogWrite() to RED1 etc...
up to Sequence 4-12: Row 4 - analogWrite() to BLUE4
But I fear that in practice it doesn't make any sense...
Am I going in the right direction?
Thanks