The generator matrix 1 0 1 1 1 0 1 1 0 1 1 0 1 1 0 1 X 1 1 1 0 1 1 X 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 X+1 1 1 0 1 X+1 0 1 X 1 X+1 X+1 0 1 X+1 X 1 X+1 X+1 X+1 X+1 1 X+1 X+1 1 1 1 1 X+1 0 0 X 0 0 0 0 0 0 X 0 X X X 0 X 0 X X 0 0 X 0 X 0 0 0 X X 0 X X X X 0 0 0 0 0 X 0 0 0 X 0 X X X X 0 X 0 X X 0 X 0 X X X 0 0 X X 0 X X 0 X X X 0 0 0 0 0 X 0 0 0 0 X X X 0 X X 0 X X X X X 0 X 0 X 0 0 0 0 0 X X X 0 0 0 0 0 0 0 0 X 0 X 0 X 0 0 X X X X X X 0 X X X X 0 0 X 0 0 X 0 0 X X X X X 0 0 0 0 0 0 X X X X 0 X 0 X X X 0 0 0 X 0 X 0 X X X 0 X 0 X X X 0 X X X generates a code of length 36 over Z2[X]/(X^2) who´s minimum homogenous weight is 32. Homogenous weight enumerator: w(x)=1x^0+203x^32+128x^36+166x^40+12x^48+2x^56 The gray image is a linear code over GF(2) with n=72, k=9 and d=32. As d=32 is an upper bound for linear (72,9,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 9. This code was found by Heurico 1.16 in 1.19 seconds.