The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X X^3+X^2  1  1  X  1 X^3  1  1  1  1  1  1  1  1 X^3  1 X^3+X^2  1  X  1  X  X
 0  X  0 X^3+X^2+X X^2 X^2+X X^3+X^2  X X^3  0 X^2+X X^2+X X^2 X^2 X^3+X  X X^2+X  X X^3+X  X  0 X^2 X^3+X^2+X X^2+X  X  X  X X^3+X X^3 X^3 X^3+X^2+X  0 X^3+X X^2 X^2  X X^3  X  0 X^3+X X^2+X
 0  0 X^3+X^2  0 X^2  0  0 X^3  0 X^2 X^2 X^2 X^2 X^3 X^3+X^2 X^2 X^3+X^2 X^3 X^2 X^3  0 X^3 X^3+X^2  0  0  0 X^3+X^2 X^3 X^3+X^2 X^2  0 X^3 X^3+X^2 X^3+X^2 X^3 X^2 X^2  0 X^3+X^2  0 X^2
 0  0  0 X^3+X^2  0  0 X^3 X^2 X^2 X^2 X^2 X^3 X^3+X^2 X^2  0 X^2 X^3+X^2  0 X^3+X^2 X^3 X^3 X^3+X^2 X^3 X^3 X^3+X^2 X^2 X^3 X^3+X^2  0 X^3+X^2 X^3 X^3 X^2  0 X^3+X^2 X^2  0 X^2 X^3 X^3 X^3+X^2
 0  0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3  0 X^3  0  0  0  0  0 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0 X^3  0  0  0  0 X^3  0 X^3 X^3 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+161x^36+96x^37+432x^38+280x^39+975x^40+304x^41+960x^42+224x^43+382x^44+112x^45+98x^46+8x^47+40x^48+12x^50+8x^52+2x^54+1x^60

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 0.266 seconds.