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

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+240x^46+32x^47+222x^48+224x^49+618x^50+224x^51+223x^52+32x^53+220x^54+10x^58+1x^60+1x^88

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 27.1 seconds.