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

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+28x^36+172x^37+52x^38+216x^39+50x^40+988x^41+47x^42+288x^43+44x^44+116x^45+28x^46+8x^47+5x^48+4x^49+1x^74

The gray image is a linear code over GF(2) with n=328, k=11 and d=144.
This code was found by Heurico 1.16 in 0.093 seconds.