The generator matrix

 1  0  0  1  1  1  0  1  1  X
 0  1  0  1  X X+1  1  0  X  0
 0  0  1  1  1  0 X+1  X  X  0
 0  0  0  X  0  X  X  X  X  X

generates a code of length 10 over Z2[X]/(X^2) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+56x^8+24x^10+36x^12+8x^14+3x^16

The gray image is a linear code over GF(2) with n=20, k=7 and d=8.
As d=8 is an upper bound for linear (20,7,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 7.
This code was found by Heurico 1.16 in 0.00052 seconds.