The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X^2  1  1 X^3+X  1  1 X^3  1  1 X^3+X^2+X  1  1  1  1 X^2  X  1  1  1  1  1  1  1  1  1  1  1  1
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2 X^3+X^2+X+1  1 X^3+X X^3+1  1 X^3 X^3+X+1  1 X^3+X^2+X X^3+X^2+1  1 X^2 X^2+X+1  X  1  1  1  0 X^2+X X^3+X^2 X^3+X X^3 X^3+X^2+X X^2  X X+1 X^2+1 X^3+X^2+X+1  0

generates a code of length 36 over Z2[X]/(X^4) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+44x^35+164x^36+44x^37+1x^38+1x^50+1x^56

The gray image is a linear code over GF(2) with n=288, k=8 and d=140.
This code was found by Heurico 1.16 in 3.62e-008 seconds.