The generator matrix

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

generates a code of length 41 over Z2[X]/(X^4) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+432x^38+712x^39+799x^40+704x^41+456x^42+424x^43+246x^44+144x^45+156x^46+18x^48+4x^50

The gray image is a linear code over GF(2) with n=328, k=12 and d=152.
This code was found by Heurico 1.16 in 0.469 seconds.