The generator matrix
1 0 1 1 1 0 1 1 1 1
0 1 1 0 1 1 0 0 0 0
0 0 X 0 0 0 0 0 0 X
0 0 0 X 0 0 0 0 0 X
0 0 0 0 X 0 0 0 0 X
0 0 0 0 0 X 0 0 0 X
0 0 0 0 0 0 X 0 0 X
0 0 0 0 0 0 0 X 0 X
0 0 0 0 0 0 0 0 X X
generates a code of length 10 over Z2[X]/(X^2) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+53x^4+48x^6+586x^8+672x^10+586x^12+48x^14+53x^16+1x^20
The gray image is a linear code over GF(2) with n=20, k=11 and d=4.
This code was found by Heurico 1.16 in 0.0113 seconds.