The generator matrix

 1  0  0  1  1  1 X^3 X^2  1  1  0  1  1  0  X  1  1 X^2+X  1  1 X^3+X X^3+X^2+X X^3+X  1 X^2  1  1  1  1 X^2+X  1 X^3+X^2+X  1  1 X^2  1
 0  1  0  0 X^3+X^2+1 X^3+X^2+1  1  X X^3 X^2+1  1 X^3 X^2+1  1  1  X X+1  1 X^3+X^2+X X^3+X^2+X+1 X^3+X^2+X X^2  1 X^3+X^2+X+1  1  1 X^3+X+1 X^3+X^2+X+1  X  1 X^2  1  X X+1  1 X^3+X^2+X
 0  0  1 X+1 X^2+X+1 X^2 X^2+X+1  1 X^3+X^2+X X^3+1 X^3+1 X^3+X^2+1 X^3+X X^2+X  X  X X^3  1 X^2+X+1 X^3+X+1  1  1  0 X^3+X^2+1  1 X^2 X^3+X^2+X  1 X^3+X^2+1 X^3+X^2+X+1 X^3+X^2+X+1 X^2+1 X^3+X^2+X+1 X^2 X^3+X^2 X^3+X+1
 0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3  0  0 X^3  0 X^3 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+208x^32+722x^33+1176x^34+1358x^35+1583x^36+1260x^37+838x^38+624x^39+309x^40+42x^41+30x^42+26x^43+11x^44+4x^46

The gray image is a linear code over GF(2) with n=288, k=13 and d=128.
This code was found by Heurico 1.16 in 0.656 seconds.