The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2  1  1  0  1  X X^2
 0  X X^3+X^2 X^2+X  0 X^2+X X^3+X^2 X^3+X  0 X^2+X X^3+X^2 X^3+X X^2 X^3+X  0 X^2+X X^3+X^2+X X^3 X^3+X^2 X^3+X  0 X^3 X^2+X X^2+X X^3+X  X X^3+X^2+X  0 X^3+X^2 X^3+X^2 X^2  X  X X^2 X^2+X X^3+X^2
 0  0 X^3  0  0  0  0 X^3  0 X^3  0 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0
 0  0  0 X^3  0  0  0 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0  0  0  0
 0  0  0  0 X^3  0  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0  0
 0  0  0  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0  0  0  0  0 X^3 X^3  0  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+162x^32+192x^33+176x^34+320x^35+376x^36+192x^37+416x^38+64x^39+116x^40+16x^42+16x^44+1x^64

The gray image is a linear code over GF(2) with n=288, k=11 and d=128.
This code was found by Heurico 1.16 in 0.078 seconds.