The generator matrix 1 0 1 1 1 X^2 1 1 0 1 1 0 1 1 X^2 1 1 X^2 1 X^2 1 X 1 1 1 X^2 1 X 1 1 X^2 1 X 1 1 X X^2 1 X 1 1 X^2+X 1 0 0 1 1 1 1 1 1 X X^2+X 1 X 1 X^2+X 1 X 1 X^2 1 X^2+X 1 1 0 1 X^2 0 1 0 0 1 1 1 1 X 1 1 X^2 1 1 1 1 X^2 1 X X^2+X 1 0 X 0 1 1 0 1 1 X^2 X+1 1 1 0 1 X+1 0 1 X+1 0 1 X+1 1 0 1 0 X^2+1 X^2 1 1 1 X X^2+X 1 X^2+X+1 1 X^2+X X+1 1 1 X^2+X 1 X^2+1 X 1 X^2+1 1 1 X^2 X^2+1 X^2 X+1 X^2+1 X^2+X 1 1 X 1 X^2+X+1 1 0 1 X^2+1 1 X^2+X 1 X^2+X+1 1 1 X+1 1 1 1 1 1 X^2+X X^2+X+1 X 1 1 X^2+1 X+1 1 1 X^2+X X^2 X^2+X+1 1 X^2+X 0 1 X^2+X 0 X^2+X 0 0 X 0 0 0 0 0 0 0 0 0 0 X^2+X X^2+X X X X^2+X X^2+X X X^2+X X^2+X X^2+X X X^2 X^2 X^2 X X^2 X^2 X^2+X X^2+X X^2+X X^2 X^2 X^2 X^2 X^2+X X X^2 X^2+X 0 X 0 X^2+X X^2 X^2 X^2+X 0 X X^2+X X^2+X X^2+X X^2+X X^2+X X X^2 X X^2 X X^2 X X^2 X^2 X^2+X X^2 X^2 X^2 X 0 X X 0 X X 0 X X^2+X X X^2+X X 0 X^2 X X^2 X^2 0 X^2 X X X^2 0 0 0 X 0 0 X^2 X^2 X^2+X X^2+X X X X^2+X X^2 X X^2 X^2+X X X X^2 X^2+X X^2 0 X^2+X X X^2+X 0 0 X^2 X^2 X^2+X X^2 X^2 X^2+X 0 0 0 0 X X X^2+X X X 0 X^2+X X^2+X 0 X X^2+X X X^2+X 0 X^2+X 0 X X^2 X^2+X 0 X^2+X 0 X^2 X^2 X^2 0 X^2 X^2+X X 0 0 X^2 X^2+X X^2+X X^2 X^2+X X X X X^2+X 0 0 X^2+X X X^2+X X X X^2 X^2+X 0 X^2+X X^2+X X^2 0 0 0 0 X X^2+X X^2+X 0 X X^2 X X^2 X^2+X X^2+X X^2+X X^2+X X^2 0 X^2 X X X^2 0 X^2+X X^2 0 X X^2 X 0 X 0 X^2+X X X^2+X X^2 X^2+X X^2+X 0 X X^2+X X X^2 X^2 X^2+X X^2 0 X^2+X X X^2+X X^2 X^2+X X^2+X X 0 X^2 0 0 X X X X^2 X^2+X X^2 X X^2+X 0 X^2 X^2+X X^2+X X^2 X X X^2 X X X^2 X^2 X 0 0 X X^2+X X X^2+X X^2+X X^2 X^2+X 0 X^2+X X^2 generates a code of length 91 over Z2[X]/(X^3) who´s minimum homogenous weight is 84. Homogenous weight enumerator: w(x)=1x^0+364x^84+496x^86+707x^88+530x^90+686x^92+466x^94+477x^96+212x^98+90x^100+14x^102+24x^104+8x^106+11x^108+6x^112+2x^114+1x^120+1x^124 The gray image is a linear code over GF(2) with n=364, k=12 and d=168. This code was found by Heurico 1.16 in 13 seconds.