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  1  1  1  1  1  1
 0 X^2  0  0  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2
 0  0 X^2  0  0  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0
 0  0  0 X^2  0  0  0 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0
 0  0  0  0 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2  0 X^2  0
 0  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0  0  0  0 X^2  0 X^2
 0  0  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2

generates a code of length 36 over Z2[X]/(X^3) who�s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+63x^32+384x^36+63x^40+1x^72

The gray image is a linear code over GF(2) with n=144, k=9 and d=64.
This code was found by Heurico 1.16 in 0.132 seconds.