edgeR: design matrix for different condition

Dear the edgeR community,

Good day.

I'm analyzing my RNA-Seq experiment with edgeR. My study has 2
different genotypes (treeHS, treeLS) and time of treatment (0H, 3H,
24H, 96H).

I first assumed that the treatment effect will be the same for each
genotype and I have the design matrix as:

  design <- model.matrix(~tree+treat)

> design
   (Intercept)  treat03H  treat24H  treat96H  treeLS
1             1        0        0        0      0
2             1        0        0        0      0
3             1        1        0        0      0
4             1        1        0        0      0
5             1        0        1        0      0
6             1        0        1        0      0
7             1        0        0        1      0
8             1        0        0        1      0
9             1        0        0        0      1
10           1        0        0        0      1
11           1        1        0        0      1
12           1        1        0        0      1
13           1        0        1        0      1
14           1        0        1        0      1
15           1        0        0        1      1