The generator matrix

 1  0  1  1 X^2  1 X^2+X  1  1  1  1  X  1  1 X^3+X^2  1 X^3+X^2  1  1  1  0  1  1  1  X  1  X  1 X^3 X^3+X^2 X^3+X^2+X  X  1  1  1  1
 0  1  1 X^2+X  1 X^2+X+1  1 X^2 X^3+X+1 X^3+X^2+1 X^3+X  1 X^2 X^3+X+1  1 X^3+X  1  1  X X+1  1 X^3+X^2 X^3+1 X^2+X  1 X^3+1 X^2+X X^3+X X^2  X  1 X^3 X^3+X X^3+X^2 X^3+X^2 X^3
 0  0  X  0 X^3+X  X X^3 X^3+X X^3+X^2 X^2 X^2+X  X X^2+X X^3+X^2+X X^3+X^2+X X^3 X^3 X^2 X^3+X  0 X^3+X^2  0 X^3+X^2+X X^2 X^2+X X^3 X^3+X X^2  X X^2+X X^3+X^2 X^3+X^2+X X^3+X^2 X^3+X^2 X^2 X^2
 0  0  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3 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+99x^32+316x^33+729x^34+616x^35+872x^36+416x^37+572x^38+248x^39+116x^40+36x^41+38x^42+32x^43+4x^46+1x^50

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.