The generator matrix 1 0 0 0 1 1 1 1 X^2+X 1 1 X^2 0 1 0 1 X X 1 1 1 1 X^2 1 X^2+X 1 0 X^2 1 X^2 1 1 1 X^2 X^2+X 1 0 1 0 X X^2+X X^2 1 X^2+X 1 0 X 1 X^2 1 1 X^2 1 1 X 0 X^2 1 1 1 X^2+X 0 X 1 1 X^2+X 0 X 1 X X^2+X X^2+X 0 1 1 1 X^2+X 1 1 0 1 1 0 1 0 1 0 0 0 X^2 1 X^2+1 1 X^2 X^2+X+1 1 X^2+X X^2+1 1 X^2+X X 1 X^2+1 X^2+1 1 0 1 X+1 X^2+X X^2 X^2 1 X^2+X 1 X^2+X+1 X^2 X+1 X^2+X 1 X+1 X^2+X X^2 1 1 X^2 0 0 X^2+X 0 1 1 X^2+X 1 X^2 X+1 1 0 X^2+X+1 1 0 1 X^2+1 X+1 X^2+X+1 1 1 X^2+X X^2+1 X X X 1 X+1 1 X X^2+X X^2+X X^2+X X^2+1 0 0 0 X 1 X X 0 0 0 0 1 0 0 X^2+1 X^2 1 1 X+1 X^2+X+1 1 1 X^2 0 0 1 X^2+X+1 X X^2 X+1 X^2+X+1 X^2+X 1 X X^2+1 1 X^2+X+1 X^2 X^2+X X^2+X X+1 X^2+1 1 X^2+X+1 X^2+X+1 X^2+X X^2+X 0 X 0 1 X^2+X+1 1 0 0 X^2+1 X^2+X 1 X^2+X+1 X+1 X^2+X X^2+X X^2+1 X^2 1 X^2 X^2+X X 1 X+1 X^2 X^2+X 1 X 1 X^2 1 X^2+1 X^2 X^2+X 1 X X+1 0 X+1 X^2 0 X^2 X^2+X+1 0 X^2+X+1 1 0 0 0 0 1 1 1 X^2+1 X 1 0 X+1 X^2+X X^2+1 X X+1 X+1 X+1 1 X^2+1 X^2+X 1 X^2+X+1 1 X^2+X 1 X X X X^2+X X^2 X+1 X X^2+1 0 X^2+X+1 X^2 1 1 X+1 0 1 X^2+X+1 X^2+X+1 X^2 X^2+X X X^2+X X^2+X X^2+X 1 X^2+X X X^2+1 1 X+1 X^2+1 X^2+1 X^2 1 X^2+X+1 X X^2+1 1 0 1 X^2+X+1 1 X^2+1 X^2+X+1 0 1 X^2+X+1 1 X^2+1 X^2+X X^2+X 1 X^2+X+1 1 X X^2 X X^2+1 0 0 0 0 0 X 0 0 0 0 X X X X X X 0 0 X^2+X X X^2 X^2 X^2+X 0 X X^2+X X^2 X^2+X X^2 X^2+X X^2+X X^2 X^2 X X^2 0 X^2 X^2+X X X^2 X^2 0 X X X X^2+X X^2+X X^2 X^2 0 X^2+X X X^2+X 0 X^2+X X^2+X X^2 X^2 X X X^2+X X^2+X X^2+X 0 X^2 X^2+X X^2+X 0 X^2 0 0 X X^2 0 0 0 0 X X^2 X X 0 X^2 0 0 generates a code of length 84 over Z2[X]/(X^3) who´s minimum homogenous weight is 75. Homogenous weight enumerator: w(x)=1x^0+136x^75+416x^76+648x^77+907x^78+938x^79+1165x^80+1212x^81+1135x^82+1254x^83+1115x^84+1226x^85+1246x^86+1158x^87+889x^88+814x^89+736x^90+492x^91+363x^92+204x^93+147x^94+84x^95+45x^96+18x^97+21x^98+2x^99+2x^100+6x^101+4x^104 The gray image is a linear code over GF(2) with n=336, k=14 and d=150. This code was found by Heurico 1.13 in 5.27 seconds.