The generator matrix
1 1 1 1 X 1 X X 0 1 1
0 X 0 0 X 0 X X X X X
0 0 X 0 X X X 0 0 X X
0 0 0 X X X 0 X 0 0 X
generates a code of length 11 over Z2[X]/(X^2) who´s minimum homogenous weight is 9.
Homogenous weight enumerator: w(x)=1x^0+8x^9+6x^10+6x^12+8x^13+2x^14+1x^16
The gray image is a linear code over GF(2) with n=22, k=5 and d=9.
This code was found by Heurico 1.16 in 0.000752 seconds.