The generator matrix

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

generates a code of length 48 over Z2[X]/(X^4) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+110x^43+233x^44+328x^45+474x^46+620x^47+704x^48+602x^49+413x^50+268x^51+155x^52+64x^53+44x^54+40x^55+19x^56+14x^57+4x^58+2x^59+1x^74

The gray image is a linear code over GF(2) with n=384, k=12 and d=172.
This code was found by Heurico 1.16 in 0.282 seconds.