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  1  1  1  X
 0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  2  2  0  0  2  2  0  0  2  2  0  2  0  2  0  2  2
 0  0  2  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  0  2  2  0  0  2  2  2  2  0  0  0  0  0  0  0  0  0  2  2  0  0  2  2  0  2  2  2  0  0  2  0  0  2  0  2
 0  0  0  2  0  0  0  2  2  2  2  2  0  2  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  0  0  2  2  0  0  2  2  0  0  2  0  2  2  2  2  2  2  2  2  2
 0  0  0  0  2  0  2  2  2  0  0  0  0  2  2  2  2  0  0  0  2  2  2  2  2  2  0  0  0  0  2  2  0  0  2  2  2  0  0  2  0  0  2  2  2  2  2  2  2  0  0  2  2  0  2
 0  0  0  0  0  2  2  0  2  2  0  2  2  2  0  0  2  0  2  2  2  0  0  2  0  2  2  0  0  2  2  0  0  2  2  0  0  0  0  2  2  2  0  0  2  0  0  0  2  2  0  2  0  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+25x^52+32x^54+128x^55+59x^56+10x^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 0.0666 seconds.