The generator matrix
1 0 0 0 0 1 1 1 0 1 1
0 1 0 0 0 0 1 1 1 0 0
0 0 1 0 0 1 1 0 1 0 0
0 0 0 1 0 1 0 1 1 0 0
0 0 0 0 1 1 0 0 0 X 0
0 0 0 0 0 X 0 0 X X 0
0 0 0 0 0 0 X 0 X 0 0
0 0 0 0 0 0 0 X X 0 0
generates a code of length 11 over Z2[X]/(X^2) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+70x^4+370x^6+1276x^8+2354x^10+2454x^12+1190x^14+419x^16+54x^18+4x^20
The gray image is a linear code over GF(2) with n=22, k=13 and d=4.
This code was found by Heurico 1.16 in 0.127 seconds.