The generator matrix

 1  1  1  1  1  1  1  1  1  1
 0  X  0  0  0  0  0  0  0  X
 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+45x^4+210x^8+512x^10+210x^12+45x^16+1x^20

The gray image is a linear code over GF(2) with n=20, k=10 and d=4.
This code was found by Heurico 1.16 in 0.00427 seconds.