The generator matrix

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

generates a code of length 55 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+349x^50+850x^51+1710x^52+2196x^53+2087x^54+2726x^55+1932x^56+1720x^57+1314x^58+742x^59+392x^60+172x^61+100x^62+34x^63+43x^64+8x^65+5x^66+2x^68+1x^70

The gray image is a code over GF(2) with n=440, k=14 and d=200.
This code was found by Heurico 1.16 in 2.19 seconds.