The generator matrix

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

generates a code of length 46 over Z2[X]/(X^4) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+134x^43+592x^44+270x^45+161x^46+242x^47+482x^48+102x^49+13x^50+8x^51+28x^52+12x^53+1x^58+1x^62+1x^64

The gray image is a linear code over GF(2) with n=368, k=11 and d=172.
This code was found by Heurico 1.16 in 0.453 seconds.