D-Optimal value by hand

Question

I'm trying to compute the D-optimal value by hand (on R)

Based on this video

I could get the D value by

library(AlgDesign)
dat <- gen.factorial(3, 2)
mat1 <- model.matrix(~(X1 + X2), dat)
mat2 <- mat1[c(1, 8, 6), ]
det((t(data.matrix( mat2 )) %*% data.matrix(mat2)))

However, when I'm trying to get the D value from this example things go terribly wrong

dat <- gen.factorial(5, 3)
des <- optFederov(~ quad(.), dat, nTrials=15, evaluateI=F)
des$D
mtr <- model.matrix(~ quad(.), des$design)
det((t(data.matrix( mtr )) %*% data.matrix(mtr)))

Any ideas why the process to calculate the D value works in the first example but fails in the second?