The generator matrix

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

generates a code of length 48 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+24x^49+1x^50+4x^51+1x^52+1x^54

The gray image is a code over GF(2) with n=384, k=5 and d=196.
This code was found by Heurico 1.16 in 0.047 seconds.