The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+104x^49+297x^50+332x^51+453x^52+414x^53+437x^54+342x^55+345x^56+344x^57+309x^58+200x^59+177x^60+110x^61+127x^62+54x^63+23x^64+20x^65+6x^66+1x^72

The gray image is a code over GF(2) with n=220, k=12 and d=98.
This code was found by Heurico 1.11 in 0.279 seconds.