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 0 1 X 1 X^2 1 1 1 1 1 X 1 1 1 0 X 1 1 1 1 X 1 1 1 X 1 1 X 1 X 1 1 1 0 1 1 X^2 0 X 1 1 1 0 X 1 X^2 1 X^2 X^2 X 0 X 0 X 0 X 0 0 X X^2+X 0 X^2 X^2+X X 0 X X X^2 X^2 X^2 X^2+X X^2+X X^2+X 0 0 X X^2 X^2 X^2+X X^2 X^2+X X X X^2 X 0 X 0 X X X^2 X X^2 X 0 X^2 0 X X X X X X 0 0 X^2+X X^2 X^2+X X^2 0 X^2+X X^2 X^2+X 0 X^2+X 0 0 0 X X X^2 X^2 X^2 X X X X X^2+X X^2 X X X X X X X X X^2 X 0 0 X X 0 X^2+X X 0 X^2 X 0 X 0 X^2+X X^2 X^2+X X X^2 X^2+X 0 0 X^2 X X X 0 X^2+X X X^2 X^2+X 0 X^2 X^2 0 X^2+X X 0 X^2+X X X^2+X X^2+X X X^2 X^2 X^2 X 0 X X^2 0 X^2+X X^2+X X^2+X X X 0 0 X X X^2+X X X 0 X^2+X X^2+X 0 0 X X X^2 X^2 X 0 X^2+X 0 X 0 X^2 0 0 X X X^2+X X^2+X X X X^2+X 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 0 X^2 0 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 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 0 0 0 0 0 0 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 0 X^2 0 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 0 0 X^2 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 generates a code of length 87 over Z2[X]/(X^3) who´s minimum homogenous weight is 77. Homogenous weight enumerator: w(x)=1x^0+38x^77+84x^78+106x^79+140x^80+188x^81+212x^82+226x^83+304x^84+300x^85+348x^86+384x^87+342x^88+300x^89+242x^90+188x^91+148x^92+162x^93+77x^94+82x^95+48x^96+24x^97+47x^98+34x^99+32x^100+12x^101+10x^102+4x^103+4x^104+2x^106+4x^108+1x^110+1x^112+1x^130 The gray image is a linear code over GF(2) with n=348, k=12 and d=154. This code was found by Heurico 1.16 in 2.46 seconds.