The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  1  1  1  X  1  1  1  1  1  X  1  1 X^2  1  X  1  1 X^2 X^3  1  1 X^2
 0 X^3+X^2  0  0  0 X^2 X^3+X^2 X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^3  0 X^3+X^2 X^3 X^3+X^2  0 X^3 X^3 X^2 X^2  0  0 X^3 X^2 X^3 X^3  0 X^2
 0  0 X^3+X^2  0 X^2 X^2 X^2 X^3  0 X^3 X^2 X^3+X^2 X^2 X^2 X^3 X^3 X^2 X^2 X^3+X^2 X^3 X^3+X^2 X^3 X^3+X^2 X^3 X^2  0 X^3+X^2 X^2 X^3  0 X^3 X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2  0 X^2 X^3+X^2 X^3+X^2 X^3+X^2
 0  0  0 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3 X^3+X^2 X^2  0 X^3+X^2  0 X^3+X^2 X^2 X^3+X^2 X^3 X^2  0 X^2 X^2  0 X^2 X^3+X^2  0 X^2 X^3+X^2 X^3 X^3 X^2 X^2 X^3 X^3+X^2 X^2 X^3+X^2  0 X^3+X^2 X^3
 0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0  0  0  0  0 X^3

generates a code of length 41 over Z2[X]/(X^4) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+97x^36+24x^37+132x^38+184x^39+459x^40+344x^41+398x^42+200x^43+95x^44+16x^45+40x^46+35x^48+6x^50+16x^52+1x^64

The gray image is a linear code over GF(2) with n=328, k=11 and d=144.
This code was found by Heurico 1.16 in 0.109 seconds.