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

generates a code of length 48 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+206x^44+232x^46+256x^47+679x^48+256x^49+208x^50+194x^52+8x^54+7x^56+1x^88

The gray image is a code over GF(2) with n=384, k=11 and d=176.
This code was found by Heurico 1.16 in 3.95 seconds.