The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 X X^2 X X X X 0 1 1 X^2 1 0 1 X 1 1 0 X^2 X 1 1 X 1 X^2 X 1 X^2 1 1 1 X 0 1 X X 1 1 1 1 1 1 X X 0 X 0 X 0 0 X X^2+X 0 0 X X^2+X X^2 0 X^2+X X^2 X^2+X X^2 X X^2+X X X^2 X^2 X^2+X X^2 0 X^2+X X X^2+X X^2 X^2+X X^2+X 0 X^2+X X^2+X X^2 X^2+X X X X X^2 X X^2 X X^2 0 X^2 X X X 0 X^2+X 0 0 X X 0 X^2+X X 0 X^2+X X X X^2 X^2 X^2+X X^2 0 X X X^2 X^2+X X^2 X 0 X^2 X 0 X^2+X X^2+X 0 0 0 X X 0 X^2+X X 0 0 X^2+X X 0 X X^2 X X^2 0 X^2+X X 0 X^2+X X X^2 X X^2+X 0 0 X^2 0 X^2+X X^2+X X X^2+X X^2 X^2+X X^2 X^2 0 X^2+X X X X X X^2+X X X^2 X X X 0 0 0 X^2 0 X^2 X^2+X X^2+X X^2+X 0 X X^2 X X X^2+X X X^2+X 0 X^2+X X^2 0 0 X X X X X 0 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 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 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 0 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 generates a code of length 81 over Z2[X]/(X^3) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+143x^68+240x^70+582x^72+88x^73+710x^74+240x^75+1231x^76+448x^77+1462x^78+800x^79+1855x^80+944x^81+1718x^82+768x^83+1636x^84+512x^85+1028x^86+224x^87+788x^88+56x^89+394x^90+16x^91+306x^92+70x^94+79x^96+10x^98+25x^100+6x^104+3x^108+1x^112 The gray image is a linear code over GF(2) with n=324, k=14 and d=136. This code was found by Heurico 1.16 in 29.1 seconds.