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 1 0 X 1 X^2 X 1 X^2 0 1 0 X X X 1 X 1 0 1 X 1 1 X^2 X X X X 1 X 1 X 0 X^2 X X^2 X X^2 X X X 0 X 1 X^2 X 0 1 0 X 0 0 0 X X^2+X X 0 X^2 X^2 X X^2+X 0 X^2+X X X^2 X^2+X X^2+X 0 0 X X^2+X X^2 X^2 0 0 X^2+X X X^2+X 0 0 X^2 X X^2+X X^2+X X^2 X X^2 X^2 X^2 0 0 X X X X X X^2 0 X X^2+X X X 0 X^2 X^2+X X^2 X^2+X 0 X^2+X 0 X^2 0 0 X^2+X X X^2 X^2+X X 0 0 X 0 X X^2+X 0 0 0 0 X X X^2+X X X^2 X^2 X 0 0 X 0 X X X^2+X 0 0 0 X X^2 X X^2+X X^2 X^2+X X^2 X^2 X^2 0 X X X^2+X X X X X^2+X X^2 X^2 X X^2 X^2+X 0 X X^2+X 0 0 0 0 X^2+X X^2 0 X^2 X^2 X^2+X X 0 X^2 X X 0 X X^2+X X X^2+X X X^2 X 0 X X^2 X^2 X X^2+X X X^2+X X^2+X X^2+X X^2 0 X^2 X^2 0 X^2+X 0 X^2+X X X^2+X X X^2+X X^2+X 0 X X^2 0 X X 0 0 0 X X 0 X^2+X X 0 X 0 X X^2+X X^2+X X^2 X^2 0 X^2 X X^2+X 0 0 X^2+X X 0 0 X X^2+X 0 X X X 0 0 X^2 X X^2 X^2+X X^2 0 X X X X^2+X X^2 X^2 X^2 X X^2 X^2 X^2 X^2+X 0 X^2 X^2+X 0 0 X^2 X X^2+X X^2 X X^2+X X^2+X X X^2+X X X^2+X X^2+X X X X 0 X^2+X X^2 X^2 0 X^2 0 0 X X^2+X X^2+X X^2+X X X^2+X 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 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 0 0 0 X^2 0 0 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 X^2 X^2 X^2 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 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 0 X^2 0 X^2 0 0 X^2 0 0 0 X^2 X^2 0 0 0 X^2 0 0 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 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 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 generates a code of length 87 over Z2[X]/(X^3) who´s minimum homogenous weight is 74. Homogenous weight enumerator: w(x)=1x^0+59x^74+110x^75+193x^76+264x^77+360x^78+410x^79+583x^80+682x^81+756x^82+942x^83+1000x^84+1124x^85+1235x^86+1186x^87+1120x^88+1134x^89+990x^90+962x^91+781x^92+614x^93+489x^94+354x^95+319x^96+226x^97+132x^98+110x^99+78x^100+44x^101+66x^102+18x^103+16x^104+6x^105+7x^106+4x^107+4x^108+2x^109+1x^110+1x^112+1x^118 The gray image is a linear code over GF(2) with n=348, k=14 and d=148. This code was found by Heurico 1.16 in 30.8 seconds.