The generator matrix

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

generates a code of length 46 over Z2[X]/(X^4) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+122x^42+120x^43+306x^44+308x^45+476x^46+220x^47+241x^48+84x^49+90x^50+28x^51+35x^52+8x^53+8x^54+1x^76

The gray image is a linear code over GF(2) with n=368, k=11 and d=168.
This code was found by Heurico 1.16 in 0.109 seconds.