The generator matrix

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

generates a code of length 49 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+378x^46+192x^47+371x^48+128x^49+508x^50+192x^51+202x^52+70x^54+1x^60+4x^62+1x^76

The gray image is a code over GF(2) with n=392, k=11 and d=184.
This code was found by Heurico 1.16 in 22.4 seconds.