The generator matrix

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

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+145x^32+272x^33+710x^34+572x^35+749x^36+548x^37+690x^38+260x^39+106x^40+12x^41+14x^42+13x^44+2x^46+2x^48

The gray image is a linear code over GF(2) with n=288, k=12 and d=128.
This code was found by Heurico 1.16 in 0.125 seconds.