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  X  X X^2  X  0  X  X  X X^2 X^2 X^2  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  0 X^2 X^3 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3 X^2 X^3 X^2 X^3 X^2  0 X^3+X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2  0 X^3+X^2 X^3+X^2  0 X^2 X^3+X^2 X^3  0  0 X^3  0  0
 0  0 X^3  0  0  0 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0  0  0  0  0  0 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0  0  0
 0  0  0 X^3  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0  0  0 X^3  0  0  0
 0  0  0  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3  0 X^3  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0  0 X^3 X^3  0 X^3 X^3 X^3  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+15x^44+48x^45+15x^46+164x^47+14x^48+192x^49+14x^50+24x^51+1x^52+16x^53+1x^54+4x^55+1x^56+1x^58+1x^66

The gray image is a linear code over GF(2) with n=384, k=9 and d=176.
This code was found by Heurico 1.16 in 0.078 seconds.