The generator matrix
1 1 1 1 1 1 1 1 1 1 1
0 X 0 0 0 X 0 0 X X 0
0 0 X 0 0 X 0 X X 0 0
0 0 0 X 0 X X X 0 0 0
0 0 0 0 X X X 0 0 X 0
generates a code of length 11 over Z2[X]/(X^2) who´s minimum homogenous weight is 8.
Homogenous weight enumerator: w(x)=1x^0+9x^8+6x^10+32x^11+6x^12+9x^14+1x^22
The gray image is a linear code over GF(2) with n=22, k=6 and d=8.
This code was found by Heurico 1.16 in 0.000339 seconds.