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  X X^2  1  1  1  1  X  1  X  1  X X^2  X
 0 X^3+X^2  0 X^2  0  0 X^2 X^2 X^3 X^3 X^2 X^3+X^2 X^3+X^2 X^3+X^2  0 X^3  0 X^2 X^3+X^2 X^3+X^2  0 X^2 X^3  0 X^3  0  0 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3  0  0
 0  0 X^3+X^2 X^2  0 X^3+X^2 X^3+X^2  0 X^3 X^2 X^2  0 X^3 X^2 X^3 X^3+X^2  0 X^3+X^2 X^2  0 X^3  0 X^2 X^3+X^2 X^2 X^2  0 X^3 X^3  0 X^3 X^3+X^2 X^3+X^2 X^3  0  0  0 X^3 X^2 X^3+X^2  0
 0  0  0 X^3  0  0 X^3  0  0  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3  0
 0  0  0  0 X^3  0  0  0  0 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3  0  0 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0
 0  0  0  0  0 X^3 X^3 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 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0 X^3 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+125x^36+16x^37+52x^38+192x^39+356x^40+608x^41+290x^42+192x^43+126x^44+16x^45+34x^46+27x^48+6x^50+4x^52+2x^54+1x^68

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 4.72 seconds.