The generator matrix 1 0 1 1 1 X^2 1 1 0 0 1 1 1 0 1 1 X^2 1 1 1 X^2 1 1 0 1 X^2 1 1 X 1 X^2 1 1 1 1 1 0 1 1 1 X 1 1 1 X 1 1 1 1 X^2+X X^2+X 1 X X 1 0 X 1 0 X X^2+X 1 1 X^2 0 1 1 X^2 X^2+X 1 1 0 1 1 1 1 0 1 1 X^2 X^2+X X 1 1 1 1 1 X 1 0 1 1 0 1 1 X^2 X+1 1 1 X^2 X^2+X+1 X^2 1 X^2+1 X^2 1 X^2+X+1 X^2+X 1 1 X^2 X+1 1 X^2 1 X^2+X+1 X^2+X 1 1 1 X^2+1 X^2+X X^2+X+1 0 X 1 X X+1 X^2+1 1 1 0 X^2+X+1 1 X X X+1 1 1 1 X^2 1 1 0 1 1 0 1 1 1 0 0 1 1 X+1 X 1 1 X^2+1 1 1 X^2+X+1 X X+1 X^2+X+1 1 X+1 X^2+1 X 1 1 0 X^2 X^2+X X 1 X 0 0 0 X 0 0 0 0 X^2 X^2+X X X^2+X X^2+X X^2+X X^2 0 X^2+X X X^2+X 0 X^2+X X^2 X X^2 X^2+X X^2 X^2 X^2 X^2+X X^2 X X^2+X X^2+X X^2+X X^2 X X 0 X^2 0 0 X^2 X X X^2+X X^2+X 0 X^2+X 0 X X X X^2 X^2 X X^2 X^2 0 X X^2 X^2+X X X^2 X X^2+X X^2+X X X^2+X X X^2 X^2 X^2+X X^2+X X^2 X^2+X X X^2+X X X^2+X X^2+X X X X X^2+X X^2 X^2 X 0 X^2 0 0 0 0 X 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2+X X X^2+X X^2+X X X^2+X X^2+X X X X X^2+X X^2+X X 0 0 X^2+X 0 0 X^2 0 X X^2 X X^2+X X X X^2+X 0 X X X 0 X^2 0 X X^2 X^2+X 0 X^2 X 0 X^2+X 0 X^2+X X^2+X X^2 X^2 X^2+X X X^2 X 0 X^2+X X X^2+X 0 X^2+X X^2 X^2+X 0 X X^2 X^2+X X^2 0 X^2 0 X^2 X^2 0 X^2 X 0 X^2 X^2 0 0 0 0 0 X X^2+X X^2+X X^2 X 0 0 X^2+X X X X X^2+X X^2 X X X^2 0 X^2 X^2 X X^2+X X X 0 0 X X^2 0 X X 0 X X 0 X^2 X^2+X X^2 X^2+X X X^2 X^2+X X X^2+X X X 0 X^2+X 0 0 X^2 X^2 X^2 X^2+X X^2 X^2+X 0 X^2+X X X^2 X^2+X X^2+X X^2+X X^2+X 0 X^2+X X^2 X^2+X X^2 X^2+X 0 0 0 X^2+X X X^2 X^2+X X X^2 X X X 0 0 X X^2 generates a code of length 89 over Z2[X]/(X^3) who´s minimum homogenous weight is 81. Homogenous weight enumerator: w(x)=1x^0+60x^81+154x^82+250x^83+244x^84+334x^85+350x^86+264x^87+310x^88+302x^89+316x^90+264x^91+292x^92+318x^93+209x^94+138x^95+121x^96+64x^97+14x^98+24x^99+13x^100+10x^101+11x^102+6x^104+14x^105+2x^106+2x^107+2x^109+2x^111+3x^112+1x^116+1x^120 The gray image is a linear code over GF(2) with n=356, k=12 and d=162. This code was found by Heurico 1.16 in 1.56 seconds.