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

generates a code of length 48 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+114x^46+64x^47+179x^48+64x^49+68x^50+11x^52+10x^54+1x^84

The gray image is a code over GF(2) with n=384, k=9 and d=184.
This code was found by Heurico 1.16 in 55 seconds.