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

generates a code of length 41 over Z2[X]/(X^3) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+235x^32+601x^34+8x^35+944x^36+184x^37+1600x^38+992x^39+2664x^40+1712x^41+2915x^42+1032x^43+1642x^44+152x^45+932x^46+16x^47+468x^48+211x^50+61x^52+12x^54+1x^58+1x^68

The gray image is a linear code over GF(2) with n=164, k=14 and d=64.
This code was found by Heurico 1.16 in 12.8 seconds.