The generator matrix

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

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+74x^43+173x^44+400x^45+461x^46+580x^47+686x^48+730x^49+417x^50+290x^51+159x^52+84x^53+14x^54+16x^55+5x^56+2x^57+1x^58+2x^66+1x^70

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 0.25 seconds.