The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+192x^49+1146x^50+1682x^51+3011x^52+3280x^53+5335x^54+3914x^55+5140x^56+3270x^57+2908x^58+1364x^59+923x^60+308x^61+175x^62+60x^63+45x^64+6x^65+4x^66+2x^67+2x^71

The gray image is a code over GF(2) with n=440, k=15 and d=196.
This code was found by Heurico 1.16 in 8.74 seconds.