The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1 X^3  1  1  1  1  1 X^3+X^2  1  X  1  X  1  0  X  1  0  X  1  X  X  1
 0  X  0  X X^3  0 X^2+X X^2+X X^2 X^2 X^3+X^2+X  X X^3+X X^3+X^2 X^2 X^2+X  X  0  X X^3+X^2+X X^3+X^2  0 X^3 X^3+X  X X^3+X^2  X X^3+X^2 X^3+X  0 X^3 X^2+X X^3 X^3+X X^2  X  X X^3 X^3+X^2+X X^3+X X^3+X^2
 0  0  X  X X^2 X^2+X X^2+X  0 X^3+X^2  X X^2 X^3+X^2+X X^2 X^3 X^2+X X^3+X  X  0 X^3 X^2+X  X X^2  X X^2+X  0 X^2 X^2+X X^3+X^2+X  0 X^2+X X^3+X^2+X X^3  X X^2+X X^2 X^3+X^2 X^3+X X^2+X X^3 X^3+X^2+X X^3+X
 0  0  0 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0  0  0  0  0  0  0  0 X^3  0 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 37.

Homogenous weight enumerator: w(x)=1x^0+60x^37+188x^38+340x^39+347x^40+394x^41+251x^42+172x^43+107x^44+88x^45+52x^46+24x^47+8x^48+10x^49+5x^50+1x^60

The gray image is a linear code over GF(2) with n=328, k=11 and d=148.
This code was found by Heurico 1.16 in 0.094 seconds.