The generator matrix 1 0 0 0 0 0 1 1 1 0 1 1 1 1 1 X 1 0 0 1 0 0 0 0 0 0 0 0 1 X 1 1 X+1 1 1 1 0 0 1 0 0 0 0 0 0 0 1 X+1 X+1 X X 0 1 X+1 0 0 0 1 0 0 0 1 1 1 0 1 X+1 X+1 1 X+1 0 1 0 0 0 0 1 0 1 1 0 1 0 0 X+1 1 X X+1 1 X 0 0 0 0 0 1 1 0 1 1 X 0 0 1 0 X X+1 0 0 0 0 0 0 0 X 0 0 X X X X X X X 0 0 0 0 0 0 0 0 0 X 0 X X 0 0 0 X X 0 0 0 0 0 0 0 0 0 0 X X X X 0 X X 0 X X generates a code of length 18 over Z2[X]/(X^2) who´s minimum homogenous weight is 10. Homogenous weight enumerator: w(x)=1x^0+258x^10+1366x^12+3384x^14+6825x^16+9100x^18+6825x^20+3384x^22+1366x^24+258x^26+1x^36 The gray image is a linear code over GF(2) with n=36, k=15 and d=10. As d=10 is an upper bound for linear (36,15,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 15. This code was found by Heurico 1.16 in 18.7 seconds.