The generator matrix

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

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+46x^44+64x^46+12x^47+314x^48+144x^49+372x^50+368x^51+820x^52+624x^53+948x^54+776x^55+1043x^56+624x^57+700x^58+368x^59+425x^60+144x^61+220x^62+12x^63+115x^64+34x^68+15x^72+3x^76

The gray image is a code over GF(2) with n=220, k=13 and d=88.
This code was found by Heurico 1.16 in 3.14 seconds.