The generator matrix
1 0 1 1 1 X^2+X 1 1 0 1 1 X^2+X 1 1 0 1 1 X^2 1 X^2+X 1 X 1 1 1 1 1 1 1 1 1 1 1 1 1 X
0 1 X+1 X^2+X X^2+1 1 0 X+1 1 X^2+X X^2+1 1 0 X+1 1 X^2+X X^2+X+1 1 X^2+1 1 1 1 X^2 X 0 X^2+X X^2 X X^2 X X^2 X X+1 X^2+X+1 X^2+X+1 0
0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0
0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0
generates a code of length 36 over Z2[X]/(X^3) who´s minimum homogenous weight is 34.
Homogenous weight enumerator: w(x)=1x^0+56x^34+64x^35+12x^36+64x^37+55x^38+2x^40+1x^48+1x^54
The gray image is a linear code over GF(2) with n=144, k=8 and d=68.
This code was found by Heurico 1.16 in 0.0144 seconds.