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 X^2  0 X^2  X  0 X^2 X^2  X  1  X  1  X  0 X^2  0  0  1
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  X X^2+X  X  X  0 X^2  0  X X^2+X  X X^2  0 X^2+X  0  X  X X^2+X  X  X  0  X X^2  X X^2 X^2+X  X  X X^2  0  0
 0  0  X  0  X  X X^2+X  0  0  0  X  X  X  0 X^2 X^2+X X^2 X^2  0 X^2+X  0  X  X X^2+X  X X^2+X  X X^2+X X^2+X X^2+X  X  X X^2 X^2  X X^2 X^2 X^2  0  X  0
 0  0  0  X  X  0 X^2+X  X X^2  X X^2  0  X X^2 X^2+X  X  0  X X^2+X  X X^2 X^2+X  0  0 X^2+X X^2+X X^2  X X^2+X  0  X X^2  X X^2+X  X X^2+X X^2 X^2  X  0  0
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0  0  0  0 X^2 X^2  0 X^2 X^2  0  0
 0  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0
 0  0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0  0  0 X^2 X^2  0  0  0  0 X^2  0
 0  0  0  0  0  0  0 X^2  0  0 X^2  0  0  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0  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+72x^32+82x^33+196x^34+284x^35+325x^36+462x^37+612x^38+760x^39+812x^40+940x^41+884x^42+760x^43+680x^44+476x^45+266x^46+216x^47+131x^48+82x^49+78x^50+28x^51+27x^52+6x^53+10x^54+2x^58

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 2.86 seconds.