The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X  0  X  X  X X^2  X X^2  X  0  X  0  X X^2  X X^2  1  1
 0  X  0 X^2+X  0 X^2+X  0  X X^2 X^2+X X^2  X X^2 X^2+X X^2  X X^2+X  X X^2+X  X  0 X^2  X  X  X  X X^2+X  X X^2+X  X  X  X  X  X  0  0
 0  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0  0  0  0
 0  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2

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+16x^34+91x^36+16x^38+2x^40+1x^48+1x^52

The gray image is a linear code over GF(2) with n=144, k=7 and d=68.
This code was found by Heurico 1.16 in 0.017 seconds.