There is an example of that kind of plot at http://docs.ggplot2.org/current/geom_boxplot.html You'd need to manipulate your matrix from wide (as you've given at postimg.org) to long format before using the code there:

library(reshape) # wide to long
library(ggplot2) # boxplots
library(magrittr) # %>%
set.seed(1) # 

# simplified version of your data.frame
dfr.wide <- data.frame(
  gene.id = as.character(1:10),
  category = sample(c('known', 'unknown'), size = 10, replace = TRUE),
  tissue.1 = rnorm(10),
  tissue.2 = rnorm(10),
  tissue.3 = rnorm(10),
  tissue.4 = rnorm(10)
  )

dfr.wide %>% head

  gene.id category   tissue.1    tissue.2    tissue.3   tissue.4
1       1    known -0.8204684 -0.04493361 -0.05612874 -0.4149946
2       2    known  0.4874291 -0.01619026 -0.15579551 -0.3942900
3       3  unknown  0.7383247  0.94383621 -1.47075238 -0.0593134
4       4  unknown  0.5757814  0.82122120 -0.47815006  1.1000254
5       5    known -0.3053884  0.59390132  0.41794156  0.7631757
6       6  unknown  1.5117812  0.91897737  1.35867955 -0.1645236

# want:
# tissue   category gene expression
# tissue.1 unknown  '1'  1.90 ...
# .
# .

dfr.long <- melt(
  dfr.wide,
  id = c('gene.id', 'category'),
  variable_name = 'tissue'
  )

dfr.long %>% head
  gene.id category   tissue      value
1       1    known tissue.1 -0.8204684
2       2    known tissue.1  0.4874291
3       3  unknown tissue.1  0.7383247
4       4  unknown tissue.1  0.5757814
5       5    known tissue.1 -0.3053884
6       6  unknown tissue.1  1.5117812

# plot it:
ggplot(
  data = dfr.long,
  aes(x = tissue, y = value)
  ) + geom_boxplot(aes(col = category))

End:

Plotting code:

You can certainly use par(mfrow=c(x,y)) where x= rows and y=columns. Run the box plots the x*y array and finally set it to par(mfrow=c(1,1)). par(mfrow(x,y)) divides the graph board in to x columns and Y rows.

Take a look to this ggplot2 tutorial that includes the code you can reuse for your own data Don't forget to revise the Aesthetics section to change the aspect of your graphics