The generator matrix

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

generates a code of length 55 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+280x^52+412x^53+290x^54+228x^55+266x^56+324x^57+120x^58+28x^59+52x^60+32x^61+4x^62+1x^64+8x^68+2x^70

The gray image is a code over GF(2) with n=440, k=11 and d=208.
This code was found by Heurico 1.16 in 0.109 seconds.