The generator matrix

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

generates a code of length 36 over Z2[X]/(X^4) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+296x^34+144x^35+251x^36+48x^37+202x^38+32x^39+43x^40+4x^42+1x^44+2x^46

The gray image is a linear code over GF(2) with n=288, k=10 and d=136.
This code was found by Heurico 1.16 in 0.515 seconds.