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  1 X^2  1  1
 0 X^3+X^2  0 X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3 X^2 X^3+X^2  0  0 X^3+X^2 X^3+X^2  0 X^3 X^3+X^2 X^2 X^3 X^3  0 X^3  0 X^2 X^2 X^2 X^2  0 X^3 X^3 X^2 X^2  0  0
 0  0 X^3+X^2 X^2  0 X^2 X^2 X^3  0 X^2 X^2  0  0 X^3+X^2 X^2 X^3 X^3 X^3  0  0 X^2 X^3+X^2 X^2 X^3 X^3 X^3 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3  0  0 X^2 X^3  0
 0  0  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3  0 X^3  0  0 X^3  0 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0
 0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3  0  0  0 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 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+53x^32+107x^34+192x^35+336x^36+192x^37+94x^38+24x^40+23x^42+1x^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 0.047 seconds.