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.