The generator matrix

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

generates a code of length 48 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+70x^42+56x^43+224x^44+428x^45+352x^46+768x^47+350x^48+872x^49+250x^50+360x^51+166x^52+76x^53+78x^54+21x^56+16x^58+5x^60+2x^62+1x^68

The gray image is a code over GF(2) with n=384, k=12 and d=168.
This code was found by Heurico 1.16 in 0.329 seconds.