The generator matrix

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

generates a code of length 6 over Z2[X]/(X^2) who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+66x^2+495x^4+924x^6+495x^8+66x^10+1x^12

The gray image is a linear code over GF(2) with n=12, k=11 and d=2.
As d=2 is an upper bound for linear (12,11,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 11.
This code was found by an older version of Heurico in 0 seconds.