The generator matrix

1 0 0 0 0 0 1 1
0 1 0 0 0 0 1 0
0 0 1 0 0 0 1 0
0 0 0 1 0 0 1 0
0 0 0 0 1 0 1 0
0 0 0 0 0 1 1 0

generates a code of length 8 over Z2[X]/(X^2) who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+30x^2+12x^3+255x^4+220x^5+488x^6+792x^7+495x^8+792x^9+502x^10+220x^11+241x^12+12x^13+36x^14

The gray image is a linear code over GF(2) with n=16, k=12 and d=2.
As d=2 is an upper bound for linear (16,12,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 12.
This code was found by Heurico 1.10 in 0 seconds.