The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1
 0  X  0  X  0  0 X+2 X+2  0  0  X  X  0  0 X+2 X+2  2  2  X X+2  2  2 X+2  X  2  2  X X+2  2  2 X+2  X  0  2  X X+2  0  0 X+2 X+2  0  X  X  2  2  X  0  X X+2 X+2  2  0  0  2  0
 0  0  X  X  0 X+2 X+2  0  2 X+2 X+2  2  2  X  X  2  2  X  X  0  2  X X+2  2  0 X+2 X+2  2  0 X+2  X  0  0  X  X  0  0 X+2  X  2  2  X  2  X  2 X+2 X+2  0  0  2 X+2  X  2  2  0
 0  0  0  2  2  2  0  2  2  0  2  0  0  2  0  2  0  0  0  0  2  2  2  2  2  2  0  0  0  0  2  2  0  0  0  0  2  2  2  2  2  2  0  2  0  0  0  2  2  0  2  0  0  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+28x^52+68x^54+64x^55+69x^56+20x^58+5x^60+1x^108

The gray image is a code over GF(2) with n=220, k=8 and d=104.
This code was found by Heurico 1.16 in 0.0842 seconds.