The generator matrix 1 0 1 1 1 X^2+X 1 1 X^2 1 X 1 1 1 0 0 1 1 X^2+X X^2+X 1 1 1 1 1 X^2+X 1 1 X^2 1 0 X X^2+X 1 1 1 0 1 1 1 1 1 X 1 X 1 1 X^2 X^2 1 X^2+X 1 1 X^2+X X 1 X^2+X 1 1 1 X^2 1 1 1 1 X^2 1 1 1 X^2+X 1 1 0 1 1 X^2+X X^2+X+1 1 0 X+1 1 X 1 X^2+1 1 X^2+X 1 1 0 X^2+X+1 1 1 X^2 X^2+X X+1 X^2+1 X+1 1 X^2 X^2+1 1 X^2+1 1 1 1 X X^2+1 X^2+X+1 1 X+1 0 X^2+X X^2+X+1 1 1 X 1 1 X^2+X 1 1 X^2+X+1 1 X^2+X X^2+X 1 0 X^2+X 1 X^2+X+1 X^2+1 X+1 1 X+1 X X^2 X^2 1 X X^2 X^2 1 X^2 X^2 0 0 X 0 X^2+X 0 X^2+X X^2 X X X^2+X 0 X X^2 0 X^2+X 0 X X^2+X X^2 X X X^2 X^2 0 0 X X^2+X X 0 X X X^2 X X^2 X X^2 X^2+X X^2 X^2 X^2 X^2+X X^2+X X^2+X 0 0 X^2 X^2 0 X X X^2+X X^2+X X X X X^2+X X X X X^2+X 0 0 X^2 X^2 X^2+X X^2 X X^2 0 X^2+X X 0 0 0 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 0 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 0 0 0 X^2 0 0 X^2 0 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 generates a code of length 72 over Z2[X]/(X^3) who´s minimum homogenous weight is 64. Homogenous weight enumerator: w(x)=1x^0+34x^64+108x^65+117x^66+344x^67+265x^68+426x^69+278x^70+456x^71+223x^72+416x^73+244x^74+372x^75+204x^76+300x^77+100x^78+92x^79+29x^80+24x^81+20x^82+8x^83+9x^84+2x^85+4x^86+4x^87+1x^88+4x^89+2x^90+4x^91+2x^92+2x^94+1x^98 The gray image is a linear code over GF(2) with n=288, k=12 and d=128. This code was found by Heurico 1.16 in 1.19 seconds.