The generator matrix

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

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+82x^32+156x^33+273x^34+288x^35+541x^36+260x^37+225x^38+80x^39+62x^40+40x^41+29x^42+8x^43+1x^44+1x^46+1x^56

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 0.062 seconds.