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 1 1 1 1 0 1 X^2 1 1 1 X 1 1 1 1 1 X 1 1 0 1 1 X^2 1 0 1 1 1 1 X 1 1 0 1 1 0 1 X^2 X 1 0 X 1 1 1 X^2 X 1 0 X 0 0 0 X X^2+X X X^2 X^2 X 0 0 X X X^2+X 0 0 X^2+X X X^2 X X^2+X X^2 X^2 0 X^2 X X^2+X X 0 X^2+X X X^2+X X^2 0 X X^2 X^2+X X^2 X^2 0 X 0 X^2 X 0 X X X^2 X 0 X X^2+X 0 X X^2+X 0 X^2 X 0 X^2+X X X 0 X^2+X X^2+X X X X X^2+X X X X^2 X X X 0 X X^2 X^2+X 0 X X^2 0 0 X 0 X X X 0 X^2 0 X^2+X X X^2+X 0 X^2+X 0 X^2 X^2+X X^2 X^2+X 0 X^2 X X 0 0 X X X^2 X^2+X X X^2 0 0 X 0 X^2 X X X^2+X X X^2 X^2 X X^2+X 0 X^2+X X^2+X X X 0 X^2+X X^2+X X^2 X^2 0 X^2+X X^2 X X^2 0 X X^2+X X^2 0 X^2 X^2 0 X^2 X X^2+X X X^2 X 0 X X^2 X^2+X X X^2 X X X^2+X X 0 0 0 X X 0 X X^2+X 0 X X^2 X X^2 X^2+X X 0 X^2 X X 0 X^2+X X^2 X^2+X X^2 X^2+X 0 X X^2+X 0 0 X^2 X X^2+X X^2+X 0 0 0 X^2+X X X^2+X 0 X X X^2 X^2 X^2 0 X^2 X^2 X^2 X X 0 X 0 X^2 0 0 X^2+X X X X^2+X X 0 0 X^2 0 X X^2 X^2 X X 0 X^2+X X X X^2 X^2+X X^2+X X^2 X^2 X^2+X 0 X^2+X 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 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 X^2 X^2 X^2 0 generates a code of length 84 over Z2[X]/(X^3) who´s minimum homogenous weight is 76. Homogenous weight enumerator: w(x)=1x^0+26x^76+90x^77+85x^78+136x^79+147x^80+126x^81+172x^82+180x^83+194x^84+220x^85+187x^86+112x^87+108x^88+58x^89+41x^90+26x^91+23x^92+38x^93+20x^94+18x^95+11x^96+12x^97+7x^98+4x^99+1x^100+2x^103+2x^107+1x^136 The gray image is a linear code over GF(2) with n=336, k=11 and d=152. This code was found by Heurico 1.16 in 0.811 seconds.