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

generates a code of length 49 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+286x^43+1772x^44+3306x^45+5546x^46+7562x^47+8997x^48+9992x^49+10139x^50+7584x^51+5462x^52+2854x^53+1248x^54+446x^55+206x^56+88x^57+35x^58+10x^59+2x^60

The gray image is a code over GF(2) with n=392, k=16 and d=172.
This code was found by Heurico 1.16 in 24.8 seconds.