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 X X X X X X X X X X X X X X X X 1 X X X X X X X X X X X X X X X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 X^3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 X^3 X^3 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 0 0 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 X^3 0 X^3 0 X^3 X^3 0 0 X^3 0 0 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 X^3 X^3 0 0 0 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 0 0 X^3 X^3 X^3 X^3 0 0 0 X^3 X^3 0 X^3 X^3 0 0 0 0 0 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 X^3 0 0 X^3 0 0 X^3 0 X^3 0 0 0 X^3 0 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 0 0 0 0 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 X^3 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 0 0 0 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 0 X^3 X^3 0 0 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 X^3 0 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 0 0 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 X^3 0 0 X^3 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 X^3 X^3 0 X^3 0 0 0 0 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 X^3 0 0 X^3 0 X^3 X^3 X^3 0 0 X^3 0 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 0 0 X^3 X^3 0 0 X^3 X^3 X^3 X^3 0 0 0 0 X^3 X^3 0 X^3 0 0 X^3 X^3 X^3 X^3 X^3 0 0 0 X^3 X^3 0 0 0 0 X^3 X^3 X^3 0 0 X^3 0 0 0 X^3 X^3 0 X^3 0 0 X^3 generates a code of length 86 over Z2[X]/(X^4) who´s minimum homogenous weight is 84. Homogenous weight enumerator: w(x)=1x^0+57x^84+414x^86+27x^88+10x^92+1x^108+2x^118 The gray image is a linear code over GF(2) with n=688, k=9 and d=336. This code was found by Heurico 1.16 in 0.453 seconds.