The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X 1 1 1 1 X X X 1 1 X X^2 X^2 X^2 1 1 X X X X X X X X X X X X X X^2
0 X^3 0 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 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 X^3 X^3 0 0 0 X^3 X^3 0 0 X^3 X^3 0 0
0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 0 0 0 X^3 X^3 0 0 X^3 X^3 0 0 0
generates a code of length 48 over Z2[X]/(X^4) who´s minimum homogenous weight is 48.
Homogenous weight enumerator: w(x)=1x^0+57x^48+4x^52+2x^64
The gray image is a linear code over GF(2) with n=384, k=6 and d=192.
This code was found by Heurico 1.16 in 0.046 seconds.