The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  0  X  1 X^3+X^2  1  1  1  1  1  X  X  1  1  1
 0  X  0  X  0 X^3 X^2+X  X X^2 X^2+X X^2 X^3+X^2+X X^2 X^3+X^2 X^3+X X^2+X X^3+X X^3+X^2+X X^3 X^3 X^3  X  X X^3+X  0 X^3 X^3+X X^2+X X^3+X^2 X^2 X^2+X X^2+X  X  0 X^3+X^2+X X^3+X^2+X
 0  0  X  X X^3+X^2 X^3+X^2+X X^2+X X^2 X^3+X^2 X^3  0 X^3+X^2  X X^2+X X^3+X X^2+X X^2+X  X X^2 X^3+X^2 X^3+X^2+X  0 X^3 X^3 X^2+X  X X^2+X X^3+X^2+X  X  X  0 X^3+X^2+X  X X^3+X X^2+X X^3+X
 0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0
 0  0  0  0 X^3 X^3  0  0  0 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0 X^3  0  0 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0  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+335x^32+16x^33+688x^34+528x^35+1113x^36+432x^37+616x^38+48x^39+227x^40+72x^42+18x^44+1x^48+1x^60

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 14.7 seconds.