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

generates a code of length 48 over Z2[X]/(X^4) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+66x^42+72x^44+64x^45+228x^46+448x^47+307x^48+448x^49+218x^50+64x^51+61x^52+58x^54+4x^56+4x^58+2x^60+2x^62+1x^84

The gray image is a linear code over GF(2) with n=384, k=11 and d=168.
This code was found by Heurico 1.16 in 0.703 seconds.