The generator matrix

 1  0  0  1  1  1  2 X^2+X+2  1  1  1  1  X X+2  1  X X^2+X+2  1 X^2+2  1  1  1  1 X^2+2 X+2  1  1  1 X^2  X  1  1 X^2 X^2  1  1 X^2+X X+2  1  1  1  1  X X+2 X^2  1  1 X^2+2
 0  1  0  0 X^2+3 X^2+3  1  2  0 X^2+2  1  3  1  1 X+3 X^2+X  1 X+1  1 X^2+X+2 X^2+2 X^2+X+1 X^2+X+2  1  1 X+1 X^2+X+2 X^2+X+3 X^2+X X+2 X+2 X^2+X+1 X^2+2  1 X^2 X+2  1 X^2 X+3 X^2  1  X  1  1  1 X^2+X+1 X^2+2  1
 0  0  1 X+1 X+1 X^2 X+1  1 X^2+1  X  1  X X^2+X X+1 X+3  1 X^2 X^2+X+2  3 X+2 X^2+X+1 X^2 X^2+X+1 X^2+X  1 X^2+1 X^2+2 X^2+1  1  1 X^2+X X^2+X  1 X^2  X X^2+3 X^2+X+1  1 X^2+X+3 X^2+2 X^2+2 X^2+2 X^2 X^2+X  0  1 X^2+3 X+2
 0  0  0 X^2 X^2+2  0 X^2+2 X^2  2 X^2  0 X^2+2 X^2  2 X^2+2 X^2+2  2  2 X^2+2  0  0 X^2 X^2+2  2  2  0 X^2 X^2+2  2  2 X^2  0 X^2+2 X^2  0  0 X^2+2 X^2+2  0 X^2+2 X^2  0 X^2 X^2+2 X^2  2  0 X^2+2

generates a code of length 48 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+280x^43+726x^44+1706x^45+1955x^46+2616x^47+2284x^48+2428x^49+1678x^50+1548x^51+640x^52+328x^53+104x^54+36x^55+21x^56+16x^57+14x^58+2x^61+1x^62

The gray image is a code over GF(2) with n=384, k=14 and d=172.
This code was found by Heurico 1.16 in 1.84 seconds.