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 X 0 X 0 1 1 X X^2 1 X X^2 X X 1 1 1 1 1 1 1 X 0 0 X 1 1 1 X X^2 X X^2 X X X X 1 1 1 X^2 X^2 0 0 X^2 X X 0 X 0 X X^2 1 1 1 1 X X 0 X^2 X^2 X X X
0 X 0 X^2+X X^2 X^2+X X^2 X 0 X^2+X 0 X^2+X X^2 X X^2 X 0 X^2+X 0 X^2+X X^2 X X^2 X X^2+X X X^2+X X 0 X^2+X X X 0 X X X^2 0 X X^2 X^2+X X^2 X 0 X^2+X X^2+X X X X^2+X X^2 0 X^2 X X X X 0 X^2 0 X^2 X X^2+X X 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2+X X X X 0 0 X^2 X^2 X^2+X X X X 0 0 X^2 0
0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0
generates a code of length 86 over Z2[X]/(X^3) who´s minimum homogenous weight is 86.
Homogenous weight enumerator: w(x)=1x^0+12x^86+32x^87+14x^88+4x^90+1x^96
The gray image is a linear code over GF(2) with n=344, k=6 and d=172.
This code was found by Heurico 1.16 in 0.447 seconds.