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 X^2 0 1 X 1 1 X 1 1 0 1 X^2 1 X^2 1 1 1 X^2 0
0 X 0 0 0 X X^2+X X X^2 X^2 X 0 0 X X^2+X X^2+X 0 X^2 X X^2 X X^2 X X^2 X^2 X^2 X X^2+X X X^2+X 0 X 0 0 X^2+X 0 0 X^2+X X X 0
0 0 X 0 X X X 0 X^2 0 X^2+X X X^2+X 0 X^2+X 0 X X^2 X^2 X^2+X X^2 0 0 X^2 X X 0 X^2+X 0 X X^2 X^2 X X X^2+X X X^2+X 0 X^2 X 0
0 0 0 X X 0 X X^2+X 0 X X^2 X X^2 X^2+X X 0 X^2+X 0 X^2 X^2 X^2 0 X^2+X X X^2+X 0 X X^2 X X X^2+X 0 X^2 X^2+X 0 X X^2+X X X 0 X
0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0
0 0 0 0 0 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2
generates a code of length 41 over Z2[X]/(X^3) who´s minimum homogenous weight is 36.
Homogenous weight enumerator: w(x)=1x^0+340x^36+120x^38+668x^40+368x^42+376x^44+24x^46+130x^48+20x^52+1x^64
The gray image is a linear code over GF(2) with n=164, k=11 and d=72.
This code was found by Heurico 1.16 in 40.5 seconds.