The generator matrix

 1  0  0  0  1  1  1  1  1  1
 0  1  0  0  1  0  0  0  0  0
 0  0  1  0  1  0  0  0  0  0
 0  0  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

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+34x^2+253x^4+888x^6+512x^7+1794x^8+3584x^9+2252x^10+3584x^11+1794x^12+512x^13+888x^14+253x^16+34x^18+1x^20

The gray image is a linear code over GF(2) with n=20, k=14 and d=2.
This code was found by Heurico 1.16 in 0.326 seconds.