The generator matrix

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

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+80x^36+170x^37+363x^38+374x^39+829x^40+646x^41+754x^42+326x^43+268x^44+72x^45+95x^46+66x^47+36x^48+6x^49+3x^50+2x^51+2x^52+2x^53+1x^66

The gray image is a linear code over GF(2) with n=328, k=12 and d=144.
This code was found by Heurico 1.16 in 0.203 seconds.