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 X X X 0 0 X 0 X^2 X^2 1 1 X 0 1 1 X 1 1 X X 1 1 1 0 1 1 1 1 1 0 1 X^2 X 1 X 1 1 X X X X 1 0 X 0 X 0 0 X X^2+X 0 0 X X^2+X X^2 0 X^2+X X^2+X X^2 X^2 X^2+X X X X X 0 X^2 0 X^2+X 0 0 X X^2 X X^2 X X^2+X 0 X^2 X X X X 0 X^2+X 0 X X^2 0 X X^2 0 X X^2+X X X X^2 0 X X^2+X X^2+X 0 0 X X^2 X X^2+X X X^2 0 X X^2+X X^2 X X 0 0 0 X X 0 X^2+X X 0 0 X^2+X X 0 X X^2 X 0 X^2 X 0 X X^2+X X^2 X^2+X 0 X^2+X X^2 0 X X X^2 0 X^2 X X^2+X 0 X X X X^2 X X 0 X^2+X X^2+X X^2 X^2+X X^2 X 0 X X 0 X 0 0 X X^2+X X X X X 0 X^2 X^2+X X^2+X X X 0 X X^2 0 X X^2+X 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 0 0 X^2 0 0 X^2 0 0 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 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 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 0 X^2 0 0 0 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 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 X^2 X^2 0 X^2 0 0 0 X^2 0 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 0 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 0 X^2 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 X^2 0 X^2 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 0 0 0 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 generates a code of length 74 over Z2[X]/(X^3) who´s minimum homogenous weight is 60. Homogenous weight enumerator: w(x)=1x^0+39x^60+26x^61+127x^62+110x^63+234x^64+212x^65+284x^66+542x^67+351x^68+886x^69+399x^70+2188x^71+408x^72+1988x^73+464x^74+2828x^75+404x^76+1462x^77+393x^78+1238x^79+365x^80+444x^81+241x^82+214x^83+171x^84+90x^85+98x^86+48x^87+46x^88+12x^89+34x^90+27x^92+6x^94+2x^96+1x^98+1x^102 The gray image is a linear code over GF(2) with n=296, k=14 and d=120. This code was found by Heurico 1.16 in 24.9 seconds.