The generator matrix

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

generates a code of length 41 over Z2[X]/(X^4) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+111x^40+56x^41+46x^42+32x^43+8x^45+2x^46

The gray image is a linear code over GF(2) with n=328, k=8 and d=160.
This code was found by Heurico 1.16 in 0.016 seconds.