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

generates a code of length 46 over Z2[X]/(X^4) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+70x^41+69x^42+78x^43+18x^44+300x^45+984x^46+300x^47+7x^48+78x^49+66x^50+70x^51+6x^52+1x^90

The gray image is a linear code over GF(2) with n=368, k=11 and d=164.
This code was found by Heurico 1.16 in 0.235 seconds.