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.