The generator matrix

 1  0  0  0  1  1  1  1  2  1  1 X+2  1  X  X  2  1  1  0  1  1  1  1  0 X+2  1  1  1  1 X+2  2  1  1 X+2  1  1  X X+2  1  1  0  0  2  2  X  0  0 X+2  X  1  0  1 X+2  1  1
 0  1  0  0  0  2  3  1  1  0  3  1  3  2  1  1 X+2  X X+2  1  2 X+1  3  1  2 X+3 X+1 X+3  2  1  X X+2 X+2  1  1  1  0 X+2  X  3  1  1  1  1  X  2 X+2  1  1 X+2  1  1  1 X+1  2
 0  0  1  0  2  1  2  3  1  3  X X+2  1  1 X+3 X+3 X+2  3  1 X+3 X+2  X X+2  X  0 X+1  1  2 X+3  2  1  2  3  0 X+1  0  1  1  X  0 X+1  3 X+2  2  1  X  0 X+3 X+3  0  X  2 X+1  X  2
 0  0  0  1 X+3 X+3 X+1  2  3 X+2  X  1  1  3  2  1  3 X+3  1  X  2  0 X+3 X+2  1  X  1 X+2  0  3  0  1 X+2  X X+1  3  X  3 X+2 X+2  X  X X+3  2 X+3  1  1  1 X+3  2  0  0 X+2  3  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+94x^49+252x^50+436x^51+327x^52+526x^53+370x^54+456x^55+321x^56+286x^57+280x^58+264x^59+129x^60+146x^61+82x^62+56x^63+22x^64+36x^65+8x^66+4x^67

The gray image is a code over GF(2) with n=220, k=12 and d=98.
This code was found by Heurico 1.16 in 0.538 seconds.