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

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+52x^44+8x^45+96x^46+184x^47+369x^48+184x^49+66x^50+8x^51+35x^52+12x^54+6x^56+2x^58+1x^84

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.