The generator matrix

 1  0  0  1  1  1 2X  1  1  0  1  1  2 3X  1 3X+2  1 2X X+2  1  1  1 X+2 3X+2 2X+2  1  1  1  X  1  1 2X  1  1  1  0 2X+2  1 X+2  1  2 3X+2  1  0  1  1  1 3X+2  1  X  1  1  1  2  1
 0  1  0 2X  3 2X+3  1  X 3X 3X X+3 3X+3  1  1  0  1 X+3  1 2X+2 3X+1  3 2X  1 3X  1  2 3X+2  0  1 3X+1 2X+3  2 3X+3 2X+2 X+1 X+2  1 3X+2  1 3X  0  1  3  1  1 3X+2 3X+3  1  3 X+2 2X+3 2X+2 3X  X 2X
 0  0  1 3X+1 X+1 2X X+1  X  3  1 2X+3 3X X+2 2X+3 3X+2  0 X+3 2X+3  1 X+2 2X+3  1 3X+1  1 3X 2X+2 3X+3  X  2  0 3X  1 2X  1 2X+1  1 2X  2 X+3 3X+3  1  X X+2 2X+1 X+2  1 2X+1 3X+2 2X+2  1 3X+3 3X+3 2X+1  0 2X+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+586x^52+856x^53+632x^54+600x^55+292x^56+400x^57+320x^58+168x^59+111x^60+72x^61+32x^62+16x^63+9x^64+1x^68

The gray image is a code over GF(2) with n=440, k=12 and d=208.
This code was found by Heurico 1.16 in 38.3 seconds.