The generator matrix 1 0 0 0 1 1 1 1 X X^2+X X 1 X^2 1 1 0 1 1 X^2 1 1 1 X 0 1 1 1 X^2 X 0 1 1 0 1 X^2+X X^2 X^2 1 X^2+X X 1 X 1 X 1 1 1 X^2 1 1 X^2 X 1 0 X^2+X 1 1 0 1 0 1 0 1 1 1 1 0 X^2+X 1 1 X^2 X^2 X X 1 1 1 1 1 1 1 1 X^2+X 1 0 1 0 0 X X X^2+X X+1 X^2+X 1 1 X^2+X+1 1 X^2+X+1 X+1 0 X^2 1 X 1 X^2 X^2+X 1 X X^2+1 X^2+X X^2+1 1 1 1 1 0 1 0 1 1 X X^2+X X^2 1 X+1 0 X 1 1 X+1 X 0 1 1 1 1 X^2 X X^2+X X^2 X X^2 X 1 X+1 X^2+X 0 X^2 X^2+1 X^2+X+1 1 X^2+X X+1 X^2+X+1 1 X^2 1 X^2+X X^2+1 X^2+1 X^2+1 X^2 X X^2+1 X^2+1 X 1 0 0 0 1 0 X X^2+X+1 X^2+X+1 X+1 1 X^2+X X+1 X^2+X X^2+1 X^2+1 X^2 1 X 0 X 0 X^2+X 1 X+1 1 X+1 X+1 1 1 X^2+X X^2 X^2+X X^2+X+1 X^2+X X^2 X^2+1 X^2+X 1 X 1 X^2+X X^2+1 1 0 1 X^2 1 X^2 X 1 X^2+1 0 1 X+1 1 0 X^2 X^2+1 1 X^2+X+1 X+1 0 1 X+1 X^2+X+1 X+1 X^2+X+1 X 1 X X^2 X X^2+X X+1 X^2+X X+1 X^2 X+1 1 X^2 X^2 X^2+X X+1 X^2+1 0 0 0 0 1 X+1 X^2+X+1 X X^2+X+1 X^2+X+1 X+1 X^2+X X^2+X 1 0 X^2+X+1 X^2+X X^2+1 X 1 X^2+1 X^2 1 X^2+X+1 X^2+X+1 X^2+X X^2 X+1 X^2+X X^2+1 X^2+X X+1 1 1 1 0 X^2 1 0 X^2 0 0 1 1 X^2+X X^2 X^2+1 X 1 X 0 X+1 X^2 0 X^2+X 1 0 X X X^2+1 X^2+1 X+1 X^2+1 X 1 X^2 0 X+1 0 X^2 X^2 X^2+X 1 X^2+X 1 1 X+1 X^2 X 0 X^2+X+1 X^2+1 0 X^2+X+1 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 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 X^2 0 0 X^2 0 X^2 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+74x^76+350x^77+420x^78+726x^79+467x^80+854x^81+430x^82+868x^83+439x^84+640x^85+427x^86+688x^87+315x^88+460x^89+259x^90+272x^91+123x^92+170x^93+87x^94+66x^95+17x^96+22x^97+7x^98+4x^99+4x^100+2x^102 The gray image is a linear code over GF(2) with n=336, k=13 and d=152. This code was found by Heurico 1.16 in 4.46 seconds.