The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  X  1  1  1  1  1  1  1  X  X  X  X  X  X  X  1  1  1  1  1  1  X  1  1
 0 2X  0  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0 2X 2X 2X 2X  0  0  0 2X 2X 2X 2X  0  0 2X 2X  0 2X 2X  0  0  0 2X  0 2X  0 2X 2X
 0  0 2X  0  0  0 2X 2X 2X 2X 2X  0 2X 2X  0  0  0  0  0 2X 2X 2X 2X  0  0  0 2X 2X 2X 2X  0  0  0 2X 2X  0 2X 2X  0  0  0 2X 2X 2X 2X  0  0  0
 0  0  0 2X  0 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0  0 2X 2X  0 2X 2X  0  0 2X  0 2X  0
 0  0  0  0 2X 2X  0 2X 2X  0 2X 2X 2X  0  0 2X  0 2X 2X  0  0  0  0 2X 2X  0 2X 2X 2X 2X  0  0  0 2X 2X  0 2X 2X  0 2X 2X  0  0  0  0  0 2X 2X

generates a code of length 48 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+252x^48+3x^64

The gray image is a code over GF(2) with n=384, k=8 and d=192.
This code was found by Heurico 1.16 in 0.047 seconds.