The generator matrix

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

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+288x^42+1782x^43+3034x^44+5872x^45+6679x^46+10060x^47+9563x^48+10810x^49+7173x^50+5690x^51+2494x^52+1388x^53+393x^54+202x^55+60x^56+26x^57+11x^58+8x^59+2x^63

The gray image is a code over GF(2) with n=384, k=16 and d=168.
This code was found by Heurico 1.16 in 26 seconds.