The generator matrix

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

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+36x^46+132x^47+198x^48+312x^49+203x^50+86x^51+33x^52+12x^53+8x^54+2x^55+1x^94

The gray image is a code over GF(2) with n=392, k=10 and d=184.
This code was found by Heurico 1.16 in 0.063 seconds.