The generator matrix 1 0 1 1 1 X^2 1 1 0 0 1 1 1 0 1 1 X^2 1 1 1 X^2 1 1 0 1 X^2+X 1 0 1 1 X^2+X 1 1 1 X^2+X 1 1 1 1 1 1 X X^2+X 1 1 X^2+X X^2+X 1 X 1 X^2+X 1 1 0 1 1 0 1 X 1 X X^2+X 1 1 1 1 X 1 1 1 1 X^2+X X^2+X 1 X 1 1 1 X^2 1 1 X^2+X 1 1 0 1 1 0 1 1 X^2 X+1 1 1 X^2 X^2+X+1 X^2 1 X^2+1 X^2 1 X^2+X+1 X^2+X 1 1 X^2 X+1 1 X^2 1 X^2+1 1 X^2+X X+1 1 X+1 X X^2+X 1 X^2+X+1 1 0 X+1 X^2+X X+1 1 1 0 X^2+X 1 1 X^2+X+1 1 X^2 1 X+1 X^2+X 1 X X^2+1 1 X^2+1 1 X^2+X 1 1 X^2+X X X^2 X^2+X 1 X 0 X^2 X^2+1 1 1 X^2+X+1 1 X^2+X+1 X^2+X+1 X+1 1 X^2 1 1 X^2 X^2 0 0 X 0 0 0 0 X^2 X^2+X X X^2+X X^2+X X^2+X X^2 0 X^2+X X X^2+X 0 X^2+X X^2 X X^2 X^2+X X^2 0 X^2 X^2+X X^2+X X^2 X^2+X X X X^2 X^2+X X^2+X X^2 X X^2 X^2+X X^2+X 0 X^2+X X^2+X X^2 0 X^2+X 0 X^2 0 X^2 X^2+X X^2 X^2 X^2+X X^2 X^2+X X 0 X^2+X 0 0 X^2 X 0 0 X 0 0 X^2+X 0 X^2+X X X^2+X X^2+X X^2 0 X^2+X X^2 0 0 X^2 0 X^2 0 0 0 X 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2+X X X^2+X X^2+X X X^2+X X^2+X X X X X^2+X X^2+X X^2 0 0 0 X^2+X X X X^2+X 0 X^2 X 0 X^2 X X^2+X X^2 X^2+X 0 0 X^2 X X^2 X X^2 X^2+X X^2+X 0 X^2 0 0 X^2+X 0 X^2 X^2+X X^2+X X 0 X^2 0 X^2+X 0 X^2+X X^2+X X^2 X 0 X^2 X X X X^2+X 0 0 X^2+X X^2+X X X^2+X X 0 0 0 0 0 X X^2+X X^2+X X^2 X 0 0 X^2+X X X X X^2+X X^2 X X X^2 0 X^2 X^2 X X^2+X X^2 X^2 X^2+X X X 0 0 X X X^2 X^2+X X^2+X 0 X X^2+X X^2 X^2 X X^2+X X^2 0 X^2+X 0 0 0 X X 0 X 0 0 0 X X 0 X^2 X^2+X X^2+X X X^2 X^2+X 0 X^2 0 0 X^2+X X X^2+X X^2 X^2 0 0 X^2 X^2 X^2+X X X^2+X 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+30x^76+144x^77+241x^78+268x^79+308x^80+294x^81+266x^82+366x^83+427x^84+364x^85+261x^86+242x^87+239x^88+192x^89+196x^90+124x^91+28x^92+12x^93+20x^94+16x^95+18x^96+10x^97+6x^98+6x^99+2x^100+8x^101+2x^103+2x^104+1x^108+1x^110+1x^118 The gray image is a linear code over GF(2) with n=336, k=12 and d=152. This code was found by Heurico 1.16 in 1.4 seconds.