You could put the squares together with lattice strips to make the backing of the quilt. Since you have 20" to work with horizontally, you could put a 2" (cut 2 1/2") vertical lattice strip between the two columns of squares. Since you have 24" to work with laterally, you could put a 2" (cut 2 1/2") horizontal lattice strip between the two rows.
This still leaves you with 4" more vertical inches. To fix this, you would do one of three things:
1. Trim 4" off the top of the original panel (front side of quilt), thus making the quilt square.
2. Add 2" (cut 2 1/2") borders to the top and bottom of the back.
3. Increase the size of the horizontal lattice strip to 6" (cut 6 1/2"). (This is my least favorite option.)