The generator matrix

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

generates a code of length 48 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+121x^48+6x^56

The gray image is a code over GF(2) with n=384, k=7 and d=192.
This code was found by Heurico 1.16 in 0.046 seconds.