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  X  0  X  1  2  2  0  X  X  1  2  X  X  X  1  1  1  0  0  1  X  1  1  1  0  1  X  0  X  X  1
 0  X  0  X  0  0  X X+2  0  2  X  0 X+2  2 X+2 X+2  0  2  X  2  X  0 X+2 X+2  X  X X+2  X  X  X  X X+2  0  0  X  0  X  2  X X+2  2  0  X  X  0  0  2  2  0  X X+2  0  2  2  0
 0  0  X  X  0 X+2  X  0  0  X  X  2  2 X+2  X  0  2  X  X X+2  0  0  2  X  X  2  2  2 X+2 X+2  2  2 X+2 X+2 X+2 X+2  X  X  X  2  X  X  X  2  X  X X+2  0  X X+2  X  X  X  X  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  2  0  0  0  2  2  2  2  2  2  2  0  2  2  0  2  0  0  2  2  0  2  2  2  0  2  2  2  2  2  0  0  0  0  2  2  0  2  0  0  0
 0  0  0  0  2  0  0  0  0  0  0  2  0  0  0  2  2  0  0  0  2  2  0  2  2  2  2  0  2  0  2  2  0  2  0  2  2  0  0  2  0  2  2  2  2  2  2  0  2  2  2  0  0  0  0
 0  0  0  0  0  2  0  0  0  2  0  0  0  0  0  2  2  2  2  2  0  2  0  2  0  2  2  2  0  0  2  0  0  0  0  0  2  0  2  2  2  0  2  2  2  0  2  2  0  0  0  2  0  0  0
 0  0  0  0  0  0  2  0  0  0  2  0  0  0  0  2  2  2  2  0  2  2  0  0  2  0  0  2  0  2  0  2  0  0  2  2  2  2  0  0  2  0  2  2  2  2  0  0  2  0  0  0  0  2  0
 0  0  0  0  0  0  0  2  0  2  2  2  2  0  0  2  2  0  2  2  0  0  2  2  2  0  0  0  0  2  2  0  0  2  0  2  0  2  0  2  2  0  0  2  0  0  0  2  0  2  2  2  2  0  0
 0  0  0  0  0  0  0  0  2  0  0  0  2  2  2  2  2  2  2  2  0  0  0  2  0  0  0  2  0  0  2  2  0  2  2  2  2  2  0  0  2  2  0  0  0  2  2  0  2  2  2  0  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+24x^44+46x^45+125x^46+140x^47+243x^48+278x^49+378x^50+448x^51+557x^52+722x^53+723x^54+844x^55+766x^56+728x^57+580x^58+452x^59+336x^60+222x^61+183x^62+152x^63+90x^64+50x^65+46x^66+12x^67+25x^68+2x^69+9x^70+4x^72+4x^74+2x^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 4.64 seconds.