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 X 0 X 0 1 1 1 X 0 X 1 1 0 1 X 1 X 0 1 0 1 1 1 X X 0 1 1 1 X 1 1 X 0 1 0 1 1 1 1 1 X X 1 0 1 1 X 1 1 1 0 X 0 X^2+X 0 X^2+X 0 X^2+X 0 X^2+X 0 X^2+X X^2+X X^2 0 X^2+X X 0 X^2+X 0 X^2 X^2+X X^2+X 0 X^2+X X^2+X X X^2+X X X^2 0 0 X^2+X X X^2+X X^2+X X X X^2 X^2+X X X^2+X X X^2+X X X^2 X^2 X^2+X X^2+X X^2+X X X^2 0 X X^2+X X^2+X X X^2+X X^2 X^2 X X^2 X^2+X X 0 0 X 0 X X X X^2 X^2+X 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 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 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 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 0 0 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 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 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 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 0 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 0 0 X^2 0 0 X^2 0 0 X^2 0 0 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 generates a code of length 76 over Z2[X]/(X^3) who´s minimum homogenous weight is 60. Homogenous weight enumerator: w(x)=1x^0+67x^60+44x^62+14x^63+182x^64+72x^65+193x^66+202x^67+321x^68+402x^69+500x^70+740x^71+840x^72+1210x^73+1227x^74+1464x^75+1479x^76+1412x^77+1274x^78+1222x^79+796x^80+812x^81+490x^82+378x^83+277x^84+170x^85+226x^86+72x^87+92x^88+18x^89+90x^90+4x^91+30x^92+34x^94+9x^96+13x^98+2x^100+2x^102+3x^106 The gray image is a linear code over GF(2) with n=304, k=14 and d=120. This code was found by Heurico 1.16 in 27.6 seconds.