The generator matrix 1 0 0 1 1 1 X^2+X X 1 1 1 1 X^2 X 0 1 1 X^2+X X^2 1 1 0 1 1 1 X 0 1 1 X 1 1 1 X^2+X 1 1 1 1 0 X^2 X^2+X 1 1 0 X X^2 1 1 X^2+X X^2+X 0 0 1 1 0 1 1 1 1 X^2+X 1 X X^2 X 0 1 X^2 1 1 1 1 1 1 1 1 X^2+X 1 1 X 1 X^2+X 1 1 0 1 0 0 1 X+1 1 X^2 X^2+X+1 X+1 X^2+X X^2+X 1 1 X^2+X X X^2+1 1 1 X^2+1 X^2 1 X^2+X+1 X^2+X X 1 X^2+X X^2+1 X+1 1 X^2 0 1 X X^2 X^2+X 1 X^2+X+1 1 1 1 X^2+X X 0 1 0 X+1 1 X 1 1 1 X X X 1 X^2+X+1 X X^2+1 1 X^2+X+1 X^2+X 1 1 0 X^2+X 1 X+1 X^2+1 X^2+1 X^2+X X 0 X^2 X^2 1 X^2+X X 1 X+1 1 1 0 0 0 1 1 1 X^2 1 1 X+1 X^2+X X^2+1 X^2+X X^2+X X+1 1 X^2+X X 1 0 X+1 1 1 X+1 0 1 X^2+X 1 X^2+X X^2 X^2+X+1 X^2+X X^2+X+1 X^2+1 1 X X+1 X X^2+X X^2+1 X^2+X 0 X^2 X^2+X+1 1 X^2+1 1 0 X 1 X^2+X+1 X X^2+X+1 X^2+X+1 X^2 1 X^2+X+1 X X^2+1 1 X^2 X 1 X^2 X^2+1 1 X^2 X^2+1 X+1 X^2 X^2+1 X+1 X+1 X+1 X^2+X+1 X X X^2+X 1 X X^2 X X^2+X+1 0 0 0 0 X X^2+X 0 X X X^2+X 0 X^2+X X^2 0 X^2+X X X X^2+X X^2 X X^2 0 X^2 0 X 0 X X^2 0 X X^2 X^2 X 0 0 X X X X^2+X 0 X X^2 X^2+X 0 X X^2 X^2 0 X^2+X X X X^2 X X^2 X^2 X 0 X X^2+X X X^2+X 0 X^2 X^2+X X^2+X X^2+X 0 X X^2+X X X^2+X 0 X X^2+X 0 X^2 X 0 X 0 X^2+X X^2 X^2+X 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 0 0 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 0 0 X^2 0 0 X^2 generates a code of length 83 over Z2[X]/(X^3) who�s minimum homogenous weight is 76. Homogenous weight enumerator: w(x)=1x^0+88x^76+170x^77+393x^78+294x^79+406x^80+368x^81+387x^82+338x^83+348x^84+234x^85+222x^86+150x^87+210x^88+118x^89+107x^90+68x^91+85x^92+20x^93+37x^94+24x^95+13x^96+2x^97+4x^98+6x^99+1x^100+2x^102 The gray image is a linear code over GF(2) with n=332, k=12 and d=152. This code was found by Heurico 1.16 in 1.3 seconds.