The generator matrix

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

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+21x^4+42x^8+128x^10+42x^12+21x^16+1x^20

The gray image is a linear code over GF(2) with n=20, k=8 and d=4.
This code was found by Heurico 1.16 in 6.29e-008 seconds.