The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  0  X  1  1  1  1  1 X^3+X^2  X  X  1  X X^3+X^2  1  1
 0  X  0  X X^3  0 X^2+X X^3+X^2+X  0 X^3 X^3+X X^3+X  0 X^3+X^2 X^3+X^2+X  X X^3+X^2  X X^3+X^2+X X^3+X^2 X^3+X  X X^3+X X^3+X  X X^3+X^2+X  0 X^3+X X^3+X^2 X^2 X^2+X X^2 X^3+X  X X^2 X^3+X^2
 0  0  X  X  0 X^3+X^2+X X^2+X X^3 X^2 X^3+X^2+X X^3+X^2+X X^2 X^3+X^2  X X^2  X X^3+X^2+X X^3+X^2+X X^3+X X^3+X^2+X  0 X^3 X^3+X^2 X^3  0 X^3+X X^3+X X^2  X  X X^2+X X^3  X  X  X  0
 0  0  0 X^2 X^3+X^2 X^2 X^3 X^2 X^2  0 X^2 X^3+X^2  0 X^3+X^2  0 X^3 X^2  0 X^2 X^3+X^2 X^2  0 X^2 X^3 X^3+X^2 X^3 X^3+X^2 X^3 X^2  0  0 X^2 X^2 X^3+X^2 X^2 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+333x^32+88x^33+692x^34+408x^35+1176x^36+456x^37+468x^38+72x^39+329x^40+52x^42+16x^44+4x^46+1x^56

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 0.391 seconds.