Question: Generate invertible 4x4 matrices over F_2

Hi, here is the code I used to try to generate all invertible 4x4 matrices over the finite field F_2 = {0.1}. However, when I look at the elements of GROUP (see below) all the elements are 4x4 matrices with a 2 in each entry. I don't know why this is?

Also, I need help converting all of the invertible 4x4 matrices in the following way: I want the 4x4 matrices to each be written as a string of length 16 with no spaces, commas or brackets. So for example the matrix

a b c d

e f g h

i j k l

m n o p

becomes abcdefghijklmnop

restart:
with(LinearAlgebra):
PRIME := 2;
2

# the group of invertible 4 x 4 matrices over the field F_p

GROUP := []:
M := Matrix([[a,b,c,d],[x,f,g,h],[y,j,k,l],[m,n,o,p]]):
for a from 0 to PRIME-1 do
for b from 0 to PRIME-1 do
for c from 0 to PRIME-1 do
for d from 0 to PRIME-1 do
for x from 0 to PRIME-1 do
for f from 0 to PRIME-1 do
for g from 0 to PRIME-1 do
for h from 0 to PRIME-1 do
for y from 0 to PRIME-1 do
for j from 0 to PRIME-1 do
for k from 0 to PRIME-1 do
for l from 0 to PRIME-1 do
for m from 0 to PRIME-1 do
for n from 0 to PRIME-1 do
for o from 0 to PRIME-1 do
for p from 0 to PRIME-1 do
if Determinant(M) mod PRIME <> 0 then
GROUP := [ op(GROUP), M ]
fi
od od od od od od od od od od od od od od od od:

nops(GROUP);
20160

GROUP;