The generator matrix

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

generates a code of length 55 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+42x^45+140x^46+192x^47+437x^48+368x^49+958x^50+704x^51+1571x^52+1102x^53+2000x^54+1292x^55+2108x^56+1158x^57+1601x^58+722x^59+850x^60+348x^61+356x^62+154x^63+133x^64+50x^65+56x^66+6x^67+19x^68+4x^69+8x^70+2x^71+1x^74+1x^80

The gray image is a code over GF(2) with n=220, k=14 and d=90.
This code was found by Heurico 1.16 in 11.8 seconds.