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 0 1 1 1 0 1 1 1 X 1 X X 1 1 1 X X^2 1 X 0 X 1 1 1 0 1 1 1 0 X X X 1 0 1 1 1 1 1 X 0 X 0 0 0 X X^2+X X 0 X^2 X^2 0 X X^2+X X X 0 X^2+X X^2 X 0 X 0 X^2 X X^2 0 0 X^2+X X^2+X X X X^2 X^2+X X X X X^2 X X^2+X X X^2+X X^2+X X 0 X X^2+X 0 X^2 X^2+X X 0 0 X^2 X^2+X 0 X X^2 X X 0 0 X X^2+X 0 X X^2 X X^2+X 0 X 0 X^2+X X^2 0 0 X 0 X X X^2+X 0 0 0 X^2+X X^2+X X X X^2 X^2 0 X^2 X^2 X X X X^2 X^2+X 0 0 X X^2+X X 0 X^2+X X^2 X^2 X X^2 X^2+X X^2 0 0 X X 0 X X^2 X^2+X X^2+X 0 0 0 X 0 X X^2 X 0 X X^2+X X^2+X X^2 X^2 X^2+X X^2+X 0 X^2 X^2+X 0 0 X X^2+X X^2 X 0 X^2+X X^2 0 0 0 X X 0 X^2+X X X^2 X^2+X X X^2 X^2 X X X^2 X^2 X^2+X X^2+X X X X^2 X^2+X 0 X X^2 0 X^2+X X^2 X^2 X X^2 X^2+X X 0 X 0 X^2+X X^2 X^2 X 0 X X^2+X X^2 X^2 X^2 0 X X^2+X X^2+X X^2 X 0 X^2 0 X^2+X 0 0 X X^2+X 0 0 0 X X X^2 X^2 X^2 X^2 X 0 X^2+X X^2+X 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 0 X^2 generates a code of length 74 over Z2[X]/(X^3) who´s minimum homogenous weight is 65. Homogenous weight enumerator: w(x)=1x^0+52x^65+114x^66+146x^67+142x^68+174x^69+270x^70+342x^71+348x^72+374x^73+399x^74+334x^75+316x^76+280x^77+198x^78+138x^79+105x^80+90x^81+77x^82+52x^83+30x^84+48x^85+28x^86+8x^87+18x^88+4x^89+1x^90+4x^91+2x^93+1x^114 The gray image is a linear code over GF(2) with n=296, k=12 and d=130. This code was found by Heurico 1.16 in 1.78 seconds.