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

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+192x^46+638x^48+192x^50+1x^96

The gray image is a linear code over GF(2) with n=384, k=10 and d=184.
This code was found by Heurico 1.16 in 11.1 seconds.