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

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+91x^32+160x^33+67x^34+384x^35+128x^39+36x^40+96x^41+60x^42+1x^66

The gray image is a linear code over GF(2) with n=144, k=10 and d=64.
This code was found by Heurico 1.16 in 0.0563 seconds.