The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+1x^46+22x^47+1x^48+6x^49+1x^50

The gray image is a linear code over GF(2) with n=368, k=5 and d=184.
This code was found by Heurico 1.16 in 0.031 seconds.