The generator matrix

 1  0  1  1  1 X^3+X^2+X  1  X  1 X^3+X^2  1  1  1  1 X^3  1  1 X^3+X^2+X  1  1 X^2+X  1  1  1  1 X^2  1  1  X  1 X^3+X  1 X^3+X^2  1  0  1
 0  1 X+1 X^2+X X^3+X^2+1  1 X^3+X^2  1 X^2+X+1  1 X^3+X^2+X X^2+1  X X^3+1  1 X^3+X+1  0  1 X^3+X X+1  1  1 X^3 X^3+1 X^2  1 X^3+X^2+X+1 X^3+X^2+X+1 X^2 X^3+X^2+X+1  1 X^3  1 X+1  X X^2+1
 0  0 X^2  0 X^3+X^2 X^2  0 X^2 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^3  0  0 X^2 X^3+X^2 X^3 X^3+X^2 X^2  0 X^3 X^3+X^2  0 X^3 X^3+X^2 X^3 X^3  0 X^3
 0  0  0 X^3  0  0  0  0 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3  0  0 X^3
 0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0  0 X^3  0  0  0  0  0  0 X^3 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+191x^32+252x^33+554x^34+656x^35+846x^36+632x^37+542x^38+240x^39+132x^40+12x^41+22x^42+8x^44+2x^46+4x^48+2x^52

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 0.141 seconds.