The generator matrix

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

generates a code of length 49 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+142x^41+692x^42+2430x^43+5558x^44+12134x^45+19181x^46+31208x^47+38080x^48+42930x^49+38031x^50+32216x^51+19403x^52+11590x^53+5203x^54+2200x^55+717x^56+272x^57+93x^58+34x^59+15x^60+4x^61+8x^63+2x^64

The gray image is a code over GF(2) with n=392, k=18 and d=164.
This code was found by Heurico 1.16 in 395 seconds.