The generator matrix

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

generates a code of length 4 over Z2[X]/(X^2) who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+28x^2+70x^4+28x^6+1x^8

The gray image is a linear code over GF(2) with n=8, k=7 and d=2.
As d=2 is an upper bound for linear (8,7,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 7.
This code was found by Heurico 1.16 in 5.7e-005 seconds.