The generator matrix

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

generates a code of length 48 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+169x^40+836x^41+2592x^42+6074x^43+11479x^44+20078x^45+29131x^46+38622x^47+43428x^48+39060x^49+30099x^50+20370x^51+10941x^52+5586x^53+2359x^54+858x^55+314x^56+70x^57+37x^58+28x^59+4x^60+6x^62+2x^65

The gray image is a code over GF(2) with n=384, k=18 and d=160.
This code was found by Heurico 1.16 in 380 seconds.