The generator matrix

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

generates a code of length 36 over Z2[X]/(X^4) who´s minimum homogenous weight is 33.

Homogenous weight enumerator: w(x)=1x^0+10x^33+90x^34+16x^35+274x^36+36x^37+69x^38+13x^40+2x^41+1x^62

The gray image is a linear code over GF(2) with n=288, k=9 and d=132.
This code was found by Heurico 1.16 in 10.9 seconds.