The generator matrix

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

generates a code of length 7 over Z2[X]/(X^2) who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+45x^2+20x^3+211x^4+240x^5+255x^6+504x^7+255x^8+240x^9+211x^10+20x^11+45x^12+1x^14

The gray image is a linear code over GF(2) with n=14, k=11 and d=2.
As d=2 is an upper bound for linear (14,11,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 11.
This code was found by Heurico 1.10 in 0 seconds.