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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  X  0  X  0  0  X  X X^2 X^2+X X^2 X^2+X X^2 X^2 X^2+X X^2+X  0 X+2 X+2 X^2 X+2 X+2  2 X^2 X^2+2  2 X^2+X+2 X^2+X X^2+2  0 X^2+X X^2+X+2 X^2+X+2  2 X+2 X^2+X+2 X^2+2  2 X+2 X^2+2  0 X^2+X X^2  X X+2 X^2+2  2 X^2+X+2
 0  0  X  X X^2+2 X^2+X X^2+X+2 X^2 X^2 X^2+X X+2  2 X^2+X+2  2 X+2 X^2+2  2  X X^2+2  X X^2+X  0 X^2 X^2+X  2 X^2+X+2 X^2+X X^2 X^2+2 X+2  X  2  0 X^2+2 X^2+X+2 X^2 X+2  2  2 X^2+X+2 X^2+X+2 X^2+X+2 X^2+2 X^2+2 X+2  0 X+2 X+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+192x^46+638x^48+192x^50+1x^96

The gray image is a code over GF(2) with n=384, k=10 and d=184.
This code was found by Heurico 1.16 in 10.9 seconds.