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

generates a code of length 41 over Z2[X]/(X^4) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+32x^37+32x^38+24x^39+226x^40+408x^41+220x^42+16x^43+28x^44+24x^45+4x^46+8x^47+1x^80

The gray image is a linear code over GF(2) with n=328, k=10 and d=148.
This code was found by Heurico 1.16 in 0.047 seconds.