The generator matrix

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

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+170x^52+288x^53+272x^54+58x^56+8x^58+86x^60+96x^61+40x^62+5x^64

The gray image is a code over GF(2) with n=220, k=10 and d=104.
This code was found by Heurico 1.16 in 5.34 seconds.