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 X^2 X X 0 X X 1 0 1 X^2 X 1 1 1 1 X 1 X 1 1 1 X 1 X 1 X 1 X 1 1 X^2 1 0 1 1 1 0 1 1 X^2 X 1 X X 0 X 0 0 0 0 0 0 X^2 X^2 X X^2+X X 0 0 X^2 X^2+X X^2+X X X X X 0 X X^2+X X 0 X X^2+X X^2 X^2+X X^2 X^2 X^2+X X 0 0 X X^2 0 X X^2 X X^2 X X X^2+X X X X X 0 X X^2 X^2+X 0 X X^2+X X 0 X^2+X X^2+X X^2+X X^2 0 X X 0 X^2 X^2 X X 0 0 X^2+X X^2 X X X X^2 X^2 X^2 0 X^2 0 0 X 0 0 0 0 0 0 0 0 0 X^2 X^2+X X^2+X X^2+X X X^2+X X^2+X X X^2 X^2 X^2+X X^2+X 0 0 X X X X^2+X X^2+X X^2+X X^2 X^2 X^2+X X X X^2 X^2 X X^2 X^2 X 0 0 X 0 X^2+X X^2 X^2+X 0 X^2 0 X X X^2+X X^2 X^2+X 0 X^2+X X^2+X X^2 X^2+X X^2 X^2 0 X X^2 X X 0 X 0 0 X^2 0 X^2+X 0 X 0 X^2 0 X X^2 0 0 0 X 0 0 X^2 X^2+X X X X X X^2 X^2+X X X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X X^2+X X X^2 X X^2+X X^2+X X X^2+X 0 X^2 0 0 0 X^2+X X^2+X X X^2+X X X^2 X X X^2+X X X^2+X X^2 X X^2 X^2 X^2+X 0 0 X^2+X X X^2+X X^2 X^2+X X^2+X 0 X^2 X^2 X^2+X X^2+X X^2 X^2+X X^2+X X^2 X^2+X X^2+X X X^2 X^2+X 0 X^2 X 0 X X^2+X X^2+X X^2 X 0 0 0 0 X 0 X^2+X X^2+X X X^2 X^2+X X^2+X 0 X X 0 X^2 X 0 X^2+X X^2+X X X^2+X X X^2 X^2 X X^2 X^2 0 X^2+X X^2 0 X^2+X X X^2+X X^2 0 X^2+X X X^2+X X^2 0 0 X X 0 0 X^2 0 0 X^2 X^2+X 0 X^2+X X X 0 X X^2 X^2 0 X^2 X 0 X X X 0 X^2 0 X 0 X^2+X X X X^2+X X X^2+X 0 X^2 X X^2 X^2+X 0 0 0 0 0 X X X^2 X^2+X X X^2+X X^2 X X 0 X 0 X^2+X X^2+X 0 X X^2 X^2 X^2+X X^2 X X^2+X X^2+X X^2 X X^2 X^2 X^2+X 0 X X^2+X 0 0 0 X X^2+X X X^2 X^2 0 0 X X^2 X X X X^2 0 X^2+X 0 0 X^2 0 X X X^2 X^2 X X X^2 X X 0 0 0 X X X^2+X 0 X^2 X^2+X 0 X^2+X 0 X 0 X^2 X X^2 generates a code of length 84 over Z2[X]/(X^3) who´s minimum homogenous weight is 74. Homogenous weight enumerator: w(x)=1x^0+220x^74+8x^75+459x^76+48x^77+508x^78+152x^79+679x^80+372x^81+850x^82+516x^83+921x^84+384x^85+804x^86+288x^87+634x^88+212x^89+392x^90+60x^91+290x^92+8x^93+172x^94+118x^96+58x^98+31x^100+4x^102+2x^108+1x^124 The gray image is a linear code over GF(2) with n=336, k=13 and d=148. This code was found by Heurico 1.16 in 76 seconds.