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

generates a code of length 48 over Z2[X]/(X^4) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+114x^46+64x^47+179x^48+64x^49+68x^50+11x^52+10x^54+1x^84

The gray image is a linear code over GF(2) with n=384, k=9 and d=184.
This code was found by Heurico 1.16 in 54.5 seconds.