The generator matrix

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

generates a code of length 55 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+140x^52+114x^54+149x^56+76x^58+27x^60+2x^62+2x^64+1x^100

The gray image is a code over GF(2) with n=220, k=9 and d=104.
This code was found by Heurico 1.16 in 0.075 seconds.