The generator matrix 1 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 1 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+42x^2+511x^4+1484x^6+1519x^8+490x^10+49x^12 The gray image is a linear code over GF(2) with n=14, k=12 and d=2. As d=2 is an upper bound for linear (14,12,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 12. This code was found by Heurico 1.10 in 0 seconds.