The generator matrix

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

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+109x^38+445x^40+358x^42+65x^44+45x^46+1x^76

The gray image is a linear code over GF(2) with n=328, k=10 and d=152.
This code was found by Heurico 1.16 in 0.078 seconds.