The generator matrix

 1  0  0  1  1  1  X  1 X^2+2  1 X+2  1  1  X  1  0  1  1 X^2  1  1  1  1 X^2+2  1 X+2 X^2+2  1 X^2+2  1 X^2+X X+2  1 X+2  1  1 X^2+2 X^2  1  1 X+2  1  1  1  1 X+2 X^2+X  1  1
 0  1  0  0 X^2+1 X^2+X+1  1 X^2+X  1  X  1  3 X^2+X+3 X^2 X+1  X X^2+X+1  2  1  0 X^2+1  1 X^2+X  1 X^2  1  1 X+1  0 X^2+3  1 X+2  2  1 X^2+3  X X^2  1  3  3  1 X^2+X+1 X+2 X^2+X+1 X^2+X  1 X^2+2  1  0
 0  0  1  1  1  0 X^2+X+1 X^2+3  2  0 X^2+1 X^2  1  1 X^2+X+1  1 X+2 X^2+X+1 X^2+X+2  X X^2+X+1 X^2+X X^2+X+2 X+1 X^2+X+3 X^2+X X^2+3 X^2+3  1 X^2+1 X^2+1  1  3 X^2 X^2+3 X^2+2  1 X^2+X+1  3 X+2  0  X X+3 X^2+X+3 X+1 X^2+3  1  X X^2
 0  0  0  X X+2 X+2 X^2+X  0 X+2 X^2+X+2  2 X^2+2 X^2 X^2+X+2 X^2  X  0  X X^2+X+2  2 X^2+X  2  X X^2+X X^2+2 X^2+2  2 X^2+X X^2+2 X^2 X^2+X+2 X^2+2 X^2 X^2 X^2+X+2  2 X^2+X X^2+2  0 X^2+X+2  X X+2  0  2 X^2+X+2  0 X^2+2 X^2+X X^2+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+118x^43+799x^44+1704x^45+2632x^46+3850x^47+4608x^48+5602x^49+4618x^50+3826x^51+2518x^52+1306x^53+712x^54+302x^55+97x^56+40x^57+14x^58+16x^59+1x^60+2x^61+2x^65

The gray image is a code over GF(2) with n=392, k=15 and d=172.
This code was found by Heurico 1.16 in 6.81 seconds.