The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X  0  X  X X^2 X^3  X  1  1  X  1  0  1 X^3  1  X  X X^2
 0  X  0 X^3+X^2+X X^2 X^2+X X^3+X^2  X X^3  0 X^2+X X^2+X X^2 X^2 X^3+X  X X^2+X  X X^3+X  X X^3+X^2+X X^3+X^2+X  X  X  X  X X^3+X^2+X X^3+X^2+X X^3+X^2  X X^2  0 X^3+X^2+X X^3+X^2+X  0 X^3
 0  0 X^3+X^2  0 X^2  0  0 X^3  0 X^2 X^2 X^2 X^2 X^3 X^3+X^2 X^2 X^3+X^2 X^3 X^2 X^3  0 X^2 X^3 X^3+X^2 X^3 X^2 X^2 X^3+X^2  0  0 X^2 X^2 X^3+X^2  0 X^3+X^2 X^3
 0  0  0 X^3+X^2  0  0 X^3 X^2 X^2 X^2 X^2 X^3 X^3+X^2 X^2  0 X^2 X^3+X^2  0 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3 X^3+X^2 X^3  0  0  0 X^3 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2
 0  0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3  0 X^3  0  0  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0 X^3  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 31.

Homogenous weight enumerator: w(x)=1x^0+124x^31+215x^32+318x^33+511x^34+596x^35+686x^36+594x^37+407x^38+284x^39+166x^40+106x^41+37x^42+20x^43+18x^44+6x^45+5x^46+2x^48

The gray image is a linear code over GF(2) with n=288, k=12 and d=124.
This code was found by Heurico 1.16 in 26.2 seconds.