The generator matrix

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

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+91x^2+1001x^4+3003x^6+3003x^8+1001x^10+91x^12+1x^14

The gray image is a linear code over GF(2) with n=14, k=13 and d=2.
As d=2 is an upper bound for linear (14,13,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 13.
This code was found by an older version of Heurico in 0 seconds.