The generator matrix 1 0 0 0 0 0 1 1 1 0 1 0 0 0 0 1 0 X 0 0 1 0 0 0 1 1 X+1 0 0 0 1 0 0 1 X 0 0 0 0 0 1 0 1 X X 0 0 0 0 0 1 1 X+1 1 generates a code of length 9 over Z2[X]/(X^2) who´s minimum homogenous weight is 4. Homogenous weight enumerator: w(x)=1x^0+113x^4+546x^6+1393x^8+1372x^10+567x^12+98x^14+6x^16 The gray image is a linear code over GF(2) with n=18, k=12 and d=4. As d=4 is an upper bound for linear (18,12,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 12. This code was found by Heurico 1.10 in 0.016 seconds.