The generator matrix 1 0 0 0 0 1 1 1 0 1 X^2 1 X^2 1 X^2+X 1 0 1 1 X 1 0 1 X^2+X 1 1 X 1 1 1 X^2+X X^2 1 1 X^2 1 1 0 X X^2 X 1 X X^2 1 1 1 1 X^2+X 0 1 0 1 X X X^2 1 1 X^2 0 0 X^2+X X^2+X X^2 0 1 X 1 1 1 X X^2 X^2 1 1 1 0 1 0 0 0 0 0 X^2 X^2 1 1 1 1 1 1 X+1 X^2+X X^2+X+1 X^2+X X X^2 1 X^2+1 1 X X 1 X^2+X+1 X^2 X^2+X+1 1 X 1 X^2+X+1 X^2 0 X+1 1 0 1 1 X 1 X X+1 X X 1 X^2 X^2 X^2+1 X^2+X 0 X X^2 1 X^2+1 0 X X^2 1 0 X 0 1 X^2+1 1 X^2+1 X^2+1 X^2+1 X^2 1 X^2+X X^2+X+1 X^2+X 0 0 0 1 0 0 X^2 1 X^2+1 1 0 1 X+1 X^2+X+1 X^2+1 0 X 1 X X^2+X+1 1 1 0 X X^2+X X^2+X 0 X^2+1 X^2+X+1 X^2 1 X^2+1 1 X+1 X^2 X X^2 X^2+X X^2+X+1 X^2+X X+1 X^2 X^2+X X+1 0 X^2+X 0 X^2+1 X^2+X 1 X^2 X+1 1 X^2 1 1 X^2 0 X^2+X 1 X X^2+X 0 1 1 X^2+1 0 X X^2+X+1 0 1 1 X 1 0 X^2+X 0 0 0 0 1 0 X^2+1 1 0 1 X^2 X^2+1 X+1 X^2 X^2+X X^2+1 X^2+X+1 X^2+X 1 0 X^2+X+1 X+1 X^2+1 X 0 X^2+X X^2+1 X+1 X 0 1 X^2 X+1 X^2+1 X X^2 X^2 X^2+1 X^2+X 1 0 1 1 X+1 1 X 0 X X+1 X^2+X X 0 X^2+X+1 X X X X^2+1 X^2+X+1 X 1 1 X^2+X 1 X+1 X X X^2+1 0 1 X^2+X X^2+X+1 X^2+1 X+1 X X^2+1 X^2+1 0 0 0 0 0 1 1 X^2 1 1 X^2+1 X^2 1 X+1 0 1 0 X^2+1 X+1 X^2+X X^2+X X^2+X+1 X X^2+X X^2+X+1 1 X^2 1 X^2+X+1 X^2+X X^2+X X^2+X X+1 X^2+X+1 X^2+1 1 X^2+X+1 X^2+1 X X^2+X+1 X^2+1 X X X+1 1 X X^2+X X^2+X+1 X^2+1 X^2+X 1 X X^2+X X X X+1 X+1 X+1 X^2+X+1 X^2+X X^2+X+1 1 X 0 X^2 X^2+X X X^2+X X^2+X+1 X^2+1 X^2+1 X+1 X+1 X^2+X+1 1 1 0 generates a code of length 76 over Z2[X]/(X^3) who´s minimum homogenous weight is 66. Homogenous weight enumerator: w(x)=1x^0+82x^66+460x^67+770x^68+1098x^69+1431x^70+1686x^71+2060x^72+2476x^73+2261x^74+2678x^75+2607x^76+2830x^77+2562x^78+2584x^79+1972x^80+1658x^81+1217x^82+900x^83+622x^84+364x^85+203x^86+116x^87+57x^88+34x^89+18x^90+6x^91+7x^92+4x^93+2x^94+2x^95 The gray image is a linear code over GF(2) with n=304, k=15 and d=132. This code was found by Heurico 1.13 in 16 seconds.