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 1 1 1 1 1 1 1 X^2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 X 1 X 1 X^2 1 0 1 1 1 1 1 X 1 1 X 1 X 1 1 X X^2 X X X^2 X^2 1 X 1 0 X 0 0 0 X^2 0 X^2 0 X X X X^2+X X^2+X X X X^2 X^2 X^2+X X^2 X^2+X X X^2+X 0 0 X 0 X^2+X X^2 X^2+X X^2+X X^2 X^2 X^2+X X^2+X X^2 X^2 X^2+X X X 0 X^2+X 0 0 X^2+X X^2 X^2 X 0 0 X X^2+X 0 X X^2 X^2 0 0 X^2+X X X^2+X X^2 X X 0 0 X^2 X X^2+X X 0 X^2 0 X 0 0 X X^2 X^2 X^2+X X X^2+X 0 0 X^2+X X^2+X X^2 X X^2 X X X^2+X X^2 X 0 X^2+X X^2 0 0 X 0 0 X^2 X X X X^2+X X X^2 X^2+X X X^2 X^2 X^2+X X 0 X 0 0 X 0 X^2+X X^2 0 X^2+X 0 X X^2+X X^2 X 0 X 0 0 0 X^2+X X X X^2 0 X^2 X^2+X X X^2+X X^2 0 X^2 X^2+X X^2 X^2+X 0 X^2+X X^2 X^2+X 0 0 X X X^2+X 0 X^2 0 X 0 X^2 0 X X^2 X^2 X X X^2 X X^2 X^2+X X X^2 X^2+X X X X^2+X X^2+X 0 X X 0 X^2+X X^2 0 X X 0 0 X 0 0 0 X 0 X X X^2+X X^2 0 0 X^2+X X X X X^2 X 0 X^2 X^2+X X X^2 X^2 X X^2 X X^2 X^2+X X 0 X 0 0 X^2+X X^2+X 0 X^2+X 0 X 0 X^2+X X X 0 X^2 X^2+X 0 X^2 X^2 X X^2 X X^2+X X 0 X^2+X X^2 X^2+X X^2 X X X X^2+X 0 0 X 0 0 X X^2+X X X^2 X^2 X^2+X X 0 X X X X^2 0 X X^2 0 X^2 0 X 0 0 X^2 X^2+X X^2 X^2 0 X^2+X 0 X^2+X 0 0 0 0 X X X^2 X X^2+X X 0 X^2+X X 0 X^2 X X^2+X X X X^2 0 X^2 0 X 0 X^2+X X 0 X^2 X^2+X X^2+X X^2 0 0 0 0 0 X^2+X X X X X X^2+X X X^2 0 X X^2 X^2 X^2+X X^2 X^2+X X^2+X X^2 X^2 X^2 X X^2+X X^2+X 0 X 0 0 X^2 X^2 X X X^2+X X^2+X X^2 0 X X^2 X^2+X X^2+X X 0 X X 0 X^2 X^2 X 0 0 X^2 X^2+X X^2+X X^2+X X^2 X^2 X^2+X X 0 X 0 X^2+X generates a code of length 97 over Z2[X]/(X^3) who´s minimum homogenous weight is 89. Homogenous weight enumerator: w(x)=1x^0+32x^89+94x^90+92x^91+113x^92+122x^93+171x^94+212x^95+169x^96+214x^97+169x^98+138x^99+140x^100+94x^101+57x^102+46x^103+36x^104+34x^105+35x^106+10x^107+15x^108+8x^109+12x^110+14x^111+6x^112+8x^113+5x^114+1x^162 The gray image is a linear code over GF(2) with n=388, k=11 and d=178. This code was found by Heurico 1.16 in 0.993 seconds.