The generator matrix

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

generates a code of length 7 over Z2[X]/(X^2) who´s minimum homogenous weight is 1.

Homogenous weight enumerator: w(x)=1x^0+14x^1+91x^2+364x^3+1001x^4+2002x^5+3003x^6+3432x^7+3003x^8+2002x^9+1001x^10+364x^11+91x^12+14x^13+1x^14

The gray image is a linear code over GF(2) with n=14, k=14 and d=1.
As d=1 is an upper bound for linear (14,14,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 14.
This code was found by an older version of Heurico in 0 seconds.