The generator matrix

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

generates a code of length 55 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+588x^49+2136x^50+3354x^51+5775x^52+7008x^53+9544x^54+8904x^55+9870x^56+6868x^57+5580x^58+3130x^59+1723x^60+640x^61+244x^62+76x^63+59x^64+16x^65+8x^66+8x^67+4x^68

The gray image is a code over GF(2) with n=440, k=16 and d=196.
This code was found by Heurico 1.16 in 30.6 seconds.