The generator matrix 1 0 0 0 1 1 1 1 X^2+X 1 1 X^2 0 1 0 X 1 1 1 1 X 1 X X^2+X X 1 0 1 X^2+X 1 X X^2 1 0 1 1 X X^2+X 1 0 0 1 1 1 1 1 1 1 1 X X^2 0 X^2+X 1 1 X 1 X^2+X X 0 X^2 1 X^2+X X^2 0 1 X 1 X^2+X 1 X X^2+X X^2+X 0 1 1 1 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 1 X X^2+X X X^2 1 X^2+1 X^2+X 1 1 X^2+1 X^2 X+1 X^2 X^2+X+1 1 1 X X^2+X X^2+X+1 X+1 X^2+X 1 X^2 X^2+X 1 X^2+1 X^2+1 X^2+1 X 0 X^2+X+1 X^2 X+1 1 1 1 0 X X^2+1 1 0 0 1 1 0 X^2+X 1 1 0 0 1 0 1 X^2+X+1 X 0 X^2+X 1 X^2 X^2+X+1 X^2+X 0 0 0 1 0 0 X^2+1 X^2 1 1 X+1 X^2+X+1 1 1 X^2 0 X^2+1 X X^2+1 X^2+X 1 X X^2+X 1 X^2 X^2+X+1 X^2+X+1 X^2+X X^2 1 X+1 X^2+X+1 X+1 1 X^2+X X^2 0 1 X^2+X X^2 1 X+1 X^2+1 X^2+X+1 X^2+X X^2 X^2 X+1 X+1 X^2+1 X^2+1 X+1 X X X+1 1 X^2+X X+1 1 X+1 X^2 1 X^2+X+1 X^2+X X 1 X^2+X X X^2+1 X X^2+1 1 1 X^2 0 X X^2+1 1 X^2 0 0 0 1 1 1 X^2+1 X 1 0 X+1 X^2+X X^2+1 X X+1 X^2+1 X+1 X X^2 X+1 X X^2+X+1 X+1 X+1 X^2 X^2 1 X^2 0 X+1 X^2+X 1 X^2+1 1 X X^2+X+1 0 X X^2+X+1 0 X+1 0 X^2+1 0 1 X^2+X 0 1 X+1 X^2+X+1 X 1 1 X X^2+X X^2 X^2+1 X^2+X+1 X X^2+1 X^2+X+1 X X X^2+X+1 X^2+X 1 0 X X^2+X+1 X^2+X+1 X^2+X X^2+1 1 X^2 X X X^2+X+1 X^2+X 0 0 0 0 X 0 0 0 0 X X X X X X X X^2 X^2 X X^2+X X^2+X X^2+X 0 X^2 0 X X^2+X X^2 X X^2 X^2 X^2+X X^2+X 0 0 X^2+X X 0 X^2 X^2+X 0 0 0 X^2 X X^2 0 X^2 X^2+X X^2+X X X 0 0 X^2+X X^2+X 0 X X X^2 X^2 X X 0 0 X X X^2 X^2+X X^2 X^2 X^2+X X^2+X X^2 0 X^2+X X^2 X generates a code of length 78 over Z2[X]/(X^3) who´s minimum homogenous weight is 69. Homogenous weight enumerator: w(x)=1x^0+112x^69+370x^70+572x^71+711x^72+986x^73+1137x^74+1190x^75+1253x^76+1388x^77+1410x^78+1246x^79+1234x^80+1116x^81+974x^82+848x^83+633x^84+416x^85+324x^86+212x^87+92x^88+74x^89+37x^90+26x^91+10x^92+4x^93+4x^94+2x^95+2x^96 The gray image is a linear code over GF(2) with n=312, k=14 and d=138. This code was found by Heurico 1.13 in 4.81 seconds.