The generator matrix

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

generates a code of length 6 over Z2[X]/(X^2) who´s minimum homogenous weight is 1.

Homogenous weight enumerator: w(x)=1x^0+12x^1+66x^2+220x^3+495x^4+792x^5+924x^6+792x^7+495x^8+220x^9+66x^10+12x^11+1x^12

The gray image is a linear code over GF(2) with n=12, k=12 and d=1.
As d=1 is an upper bound for linear (12,12,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 12.
This code was found by an older version of Heurico in 0 seconds.