The generator matrix

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

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+56x^2+16x^3+924x^4+560x^5+4040x^6+4368x^7+7366x^8+11440x^9+8008x^10+11440x^11+7324x^12+4368x^13+4088x^14+560x^15+897x^16+16x^17+64x^18

The gray image is a linear code over GF(2) with n=20, k=16 and d=2.
As d=2 is an upper bound for linear (20,16,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 16.
This code was found by Heurico 1.11 in 0.046 seconds.