The generator matrix

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

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+74x^36+160x^37+229x^38+616x^39+453x^40+1024x^41+498x^42+608x^43+224x^44+128x^45+35x^46+24x^47+13x^48+2x^50+2x^52+3x^54+1x^56+1x^62

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 0.156 seconds.