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

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+51x^32+88x^33+129x^34+262x^35+298x^36+412x^37+646x^38+718x^39+984x^40+1102x^41+920x^42+832x^43+544x^44+358x^45+303x^46+208x^47+148x^48+82x^49+47x^50+26x^51+22x^52+6x^53+2x^54+2x^55+1x^62

The gray image is a linear code over GF(2) with n=164, k=13 and d=64.
This code was found by Heurico 1.16 in 2.81 seconds.