The generator matrix

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

generates a code of length 50 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+296x^46+304x^47+672x^48+464x^49+646x^50+464x^51+666x^52+304x^53+258x^54+2x^56+10x^58+1x^60+6x^62+1x^68+1x^72

The gray image is a code over GF(2) with n=400, k=12 and d=184.
This code was found by Heurico 1.16 in 10.5 seconds.