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 X^2  1  1  1  1  1  1  1  X  X  1  1
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2 X^3 X^2  0 X^3+X^2  0 X^3+X^2  0 X^2 X^3 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^2  0  0  0  0 X^3 X^3 X^3+X^2 X^3 X^3+X^2 X^2 X^2  0  0 X^3 X^3 X^3+X^2 X^3+X^2  0  0
 0  0 X^3  0  0  0 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0  0  0  0  0  0  0 X^3 X^3
 0  0  0 X^3  0  0  0 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3  0  0  0 X^3 X^3
 0  0  0  0 X^3  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0  0  0 X^3 X^3  0  0 X^3  0 X^3  0 X^3
 0  0  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3  0 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+18x^36+92x^38+144x^40+512x^41+184x^42+21x^44+44x^46+7x^48+1x^76

The gray image is a linear code over GF(2) with n=328, k=10 and d=144.
This code was found by Heurico 1.16 in 0.062 seconds.