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

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

Homogenous weight enumerator: w(x)=1x^0+208x^46+158x^48+512x^49+352x^50+512x^51+64x^52+208x^54+32x^56+1x^96

The gray image is a code over GF(2) with n=400, k=11 and d=184.
This code was found by Heurico 1.16 in 0.735 seconds.