The generator matrix

 1  0  1  1  1  0  1  1  X  1 X+2  1  1  1  0  1  1  2  X  1  1 X+2  1  1  1  1  1  1  X  1  2  0  1  1  0  X  1  1  X  1  X  1  1  1  0  X  1  1  1 X+2 X+2  1  1  1  1
 0  1  1  0 X+1  1  X X+3  1 X+2  1  3  0 X+1  1  2 X+3  1  1 X+2  1  1  X  3  3 X+3  1  1  1  2  1  1  2  0  1  1  0 X+1  1  3  X  2 X+1 X+2  1 X+2  3  X  1  1  1  3 X+1 X+1  0
 0  0  X X+2  0 X+2  X X+2  X  0  2  0  2  0  0  X X+2 X+2  X  2  X  2 X+2  0  0  X X+2  X X+2  X X+2  0  X  2  0  X  0  2  X  0 X+2 X+2  0  0  2  X  X  2 X+2  2 X+2  X  2  0  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  0  2  2  2  0  2  0  2  2  2  2  2  0  0  2  0  0  2  0  2  0  0  0  2  2  2  0  0  2  2  0  0  2  0  2  2  0  2  0  0
 0  0  0  0  2  0  0  0  0  0  0  2  0  2  0  0  0  0  2  2  2  2  2  2  2  0  2  2  2  2  0  2  0  0  0  2  2  2  0  2  0  2  0  0  0  2  2  2  0  2  2  2  0  0  0
 0  0  0  0  0  2  0  0  0  0  0  2  2  2  0  2  2  2  2  0  0  2  0  0  2  2  2  2  2  0  0  0  0  2  2  2  0  0  0  0  2  0  2  0  0  2  2  0  0  0  2  2  2  2  0
 0  0  0  0  0  0  2  0  0  0  0  0  0  2  2  2  2  2  0  2  0  2  2  0  0  0  2  0  0  2  2  2  0  2  0  2  0  0  0  0  0  2  0  2  2  2  2  2  0  0  2  2  2  0  0
 0  0  0  0  0  0  0  2  0  2  2  0  2  0  2  2  0  2  2  0  2  2  2  0  2  0  2  0  0  0  2  0  2  2  2  0  2  0  0  2  0  0  2  2  0  2  2  2  0  2  2  0  0  0  0
 0  0  0  0  0  0  0  0  2  0  0  2  2  2  0  2  2  0  2  2  2  0  2  2  0  0  2  2  0  0  2  0  2  2  2  0  0  2  0  0  2  2  0  2  2  2  0  0  2  2  2  2  2  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+35x^44+46x^45+132x^46+156x^47+472x^48+316x^49+794x^50+720x^51+1594x^52+1156x^53+2103x^54+1340x^55+2082x^56+1212x^57+1655x^58+692x^59+794x^60+298x^61+382x^62+152x^63+111x^64+40x^65+44x^66+12x^67+22x^68+4x^69+7x^70+6x^72+3x^74+3x^76

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 11.7 seconds.