The generator matrix

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

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+134x^50+176x^51+456x^52+464x^53+622x^54+604x^55+673x^56+368x^57+174x^58+104x^59+141x^60+64x^61+74x^62+12x^63+22x^64+4x^66+2x^68+1x^84

The gray image is a code over GF(2) with n=440, k=12 and d=200.
This code was found by Heurico 1.16 in 0.375 seconds.