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 1 X 0 0 1 1 X^2 X^2 X 0 X^2 0 X^2 1 1 1 1 X^2 X 1 X 1 0 1 1 1 X X X^2 0 1 1 1 X^2 X 1 1 0 1 X 0 X X X^2 X X 1 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 0 0 X X^2+X X^2 0 X X^2+X X X X^2 X X X 0 X X^2 X 0 X X^2+X X^2 X^2 X X^2 X^2 X^2+X X^2 X X^2 X^2 0 X^2 X X X 0 X^2+X 0 X X X X X 0 0 X X 0 X^2 X^2 X^2+X X^2+X 0 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 X X^2 X^2+X X X^2 X^2+X X^2+X X^2+X X^2 X X^2 X^2 X X^2+X 0 X 0 0 X X^2+X X X 0 X^2 X^2 X^2+X 0 X^2+X X^2+X X^2 0 X^2+X X^2+X 0 X^2+X X^2+X 0 X^2+X X^2+X 0 X X^2+X 0 0 X 0 X^2 X X^2 X^2+X X X^2 0 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 0 X^2+X X^2+X X^2 X^2 X^2 X X^2+X X X^2 X^2 X^2 X^2+X 0 X^2 X^2 X X^2 X X 0 X^2+X X 0 X^2+X 0 X^2 X^2+X X X X^2 X X X^2+X X^2+X X^2+X 0 0 X^2+X 0 X X 0 X^2+X 0 X^2+X 0 0 X^2 X X^2 X^2+X 0 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 0 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 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 0 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 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 0 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 0 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 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 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 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 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 0 0 0 0 0 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 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 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 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 0 X^2 0 X^2 0 generates a code of length 89 over Z2[X]/(X^3) who´s minimum homogenous weight is 76. Homogenous weight enumerator: w(x)=1x^0+63x^76+102x^77+224x^78+236x^79+312x^80+410x^81+563x^82+678x^83+723x^84+870x^85+966x^86+1164x^87+1203x^88+1288x^89+1302x^90+1156x^91+1102x^92+988x^93+742x^94+612x^95+439x^96+330x^97+193x^98+190x^99+175x^100+86x^101+78x^102+52x^103+59x^104+20x^105+21x^106+8x^107+17x^108+2x^109+6x^110+2x^112+1x^122 The gray image is a linear code over GF(2) with n=356, k=14 and d=152. This code was found by Heurico 1.16 in 31.9 seconds.