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

generates a code of length 48 over Z2[X]/(X^4) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+57x^44+64x^46+781x^48+64x^50+54x^52+2x^56+1x^92

The gray image is a linear code over GF(2) with n=384, k=10 and d=176.
This code was found by Heurico 1.16 in 0.094 seconds.