The generator matrix

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

generates a code of length 36 over Z2[X]/(X^4) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+183x^32+64x^33+128x^34+448x^35+440x^36+448x^37+128x^38+64x^39+102x^40+39x^44+2x^48+1x^60

The gray image is a linear code over GF(2) with n=288, k=11 and d=128.
This code was found by Heurico 1.16 in 1.28 seconds.