The generator matrix 1 0 1 1 1 X^2+X X^2 1 1 X 1 1 1 1 0 1 X 1 X^2+X 1 1 1 1 0 1 1 1 1 0 1 1 X^2+X 0 1 X 1 1 X^2 1 1 1 1 0 1 X^2+X 1 X^2 1 1 1 1 1 X^2 1 1 0 1 1 1 1 1 X^2 1 0 1 0 1 X^2+X 1 1 X X 0 1 1 0 1 1 1 X^2+X X^2+X+1 1 X^2 X+1 X X^2+1 1 X 1 X^2+1 1 X^2+X+1 X^2+1 X 0 1 X^2+1 X^2 X+1 X^2 1 X^2+X+1 0 1 1 1 1 X^2+1 X^2 1 X^2+1 X^2 X^2+X+1 X 1 1 1 X^2+X+1 1 X^2+X X^2+X+1 X^2+X+1 X^2+X+1 X^2+X 1 X+1 0 1 0 X X^2 X+1 X^2+X 0 X^2+X 1 0 1 X^2+X 1 X 0 1 X 0 0 X 0 0 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X X X^2+X X^2+X X^2+X X X^2+X 0 X^2+X X X^2+X X X^2+X X X^2+X X X^2+X X^2 X 0 X^2+X X^2+X X^2+X 0 X^2 X^2 X X^2+X X^2+X 0 X X^2 X^2+X 0 X^2 X X^2 X X X X^2 X^2 X X^2+X X^2+X X^2+X 0 0 0 0 X 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2+X X X^2+X X^2+X X X^2+X X^2+X X^2+X X X^2+X X^2+X 0 X X 0 X^2+X X^2 X^2+X X^2+X X X^2 X^2 X^2 X 0 X^2+X X X^2 0 X^2 X^2 X X^2+X X^2+X X X^2+X 0 X^2+X X^2+X X^2+X X X X^2 X X X 0 X X^2 X^2 X 0 X^2+X 0 X^2 X^2 X^2+X 0 0 0 0 0 X 0 X^2+X X^2 X X X^2+X X^2 X^2+X X^2 X X 0 X^2+X X^2+X X^2 X^2 X^2 X X^2 X X^2 X^2 0 X^2+X X^2+X X 0 X X^2+X 0 0 X^2 X^2 X X^2+X 0 X^2+X X X^2+X X X^2+X X X X 0 0 0 X^2+X 0 X^2+X X^2+X X X^2 X X^2+X X^2+X X^2+X X X 0 X^2 X X^2 0 X^2+X 0 X 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 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+270x^64+68x^65+540x^66+208x^67+831x^68+372x^69+1020x^70+360x^71+1032x^72+428x^73+953x^74+320x^75+715x^76+220x^77+407x^78+72x^79+226x^80+61x^82+46x^84+25x^86+9x^88+2x^90+4x^92+2x^96 The gray image is a linear code over GF(2) with n=288, k=13 and d=128. This code was found by Heurico 1.16 in 7.1 seconds.