The generator matrix

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

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+49x^50+248x^51+398x^52+550x^53+596x^54+514x^55+620x^56+492x^57+290x^58+200x^59+58x^60+30x^61+19x^62+10x^63+11x^64+5x^66+4x^67+1x^78

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 0.265 seconds.