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

generates a code of length 55 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+68x^44+126x^45+194x^46+226x^47+442x^48+420x^49+786x^50+472x^51+1832x^52+528x^53+2888x^54+534x^55+2747x^56+636x^57+1799x^58+432x^59+865x^60+346x^61+402x^62+214x^63+167x^64+112x^65+69x^66+40x^67+18x^68+8x^69+4x^70+2x^71+3x^72+1x^74+1x^76+1x^82

The gray image is a code over GF(2) with n=220, k=14 and d=88.
This code was found by Heurico 1.16 in 15.6 seconds.