The generator matrix

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

generates a code of length 55 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+122x^48+352x^49+375x^50+680x^51+680x^52+934x^53+732x^54+862x^55+588x^56+834x^57+532x^58+502x^59+338x^60+314x^61+144x^62+90x^63+61x^64+30x^65+9x^66+10x^67+2x^68

The gray image is a code over GF(2) with n=220, k=13 and d=96.
This code was found by Heurico 1.16 in 2.15 seconds.