The generator matrix

 1  0  1  1  1  1  1  1  1  1
 0  1  1  0  0  0  0  0  0  0
 0  0  X  0  0  0  0  0  0  0
 0  0  0  X  0  0  0  0  0  0
 0  0  0  0  X  0  0  0  0  0
 0  0  0  0  0  X  0  0  0  0
 0  0  0  0  0  0  X  0  0  0
 0  0  0  0  0  0  0  X  0  0
 0  0  0  0  0  0  0  0  X  0
 0  0  0  0  0  0  0  0  0  X

generates a code of length 10 over Z2[X]/(X^2) who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+14x^2+77x^4+232x^6+434x^8+1024x^9+532x^10+1024x^11+434x^12+232x^14+77x^16+14x^18+1x^20

The gray image is a linear code over GF(2) with n=20, k=12 and d=2.
This code was found by Heurico 1.16 in 0.0167 seconds.