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  1 X^3  1  1 X^3  1  1
 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  0 X^2+X X^3+X^2 X^3+X X^3 X^3+X^2+X X^2 X^3+X  0 X^2+X X^3+X^2 X^3+X X^3+X^2 X^2+X X^2 X^3+X^2+X  0 X^3 X^3 X^3+X  X X^3  0  0
 0  0 X^3  0  0  0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0  0  0 X^3  0 X^3  0 X^3  0  0 X^3  0  0  0
 0  0  0 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0 X^3  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0  0
 0  0  0  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0  0  0 X^3 X^3  0  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0  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+43x^32+496x^34+51x^36+352x^38+20x^40+48x^42+12x^44+1x^68

The gray image is a linear code over GF(2) with n=288, k=10 and d=128.
This code was found by Heurico 1.16 in 0.031 seconds.