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 X 1 X X 0 1 1 X X X X X 1 2 1 X 1 X 1
0 X 0 0 0 0 0 0 0 0 2 X X X+2 0 X+2 X+2 0 X X X+2 X+2 X X 2 2 X 0 2 0 X X 2 X+2 0 X X 0 2 X X 2 2 X 0 X+2 X+2 X+2 2 X X X+2 2 X+2 0
0 0 X 0 0 0 0 0 0 0 X+2 2 X X X X 0 X 0 X+2 X+2 2 X 2 X 2 2 2 X+2 X+2 X 0 X+2 X X+2 0 X+2 X 2 2 2 0 X+2 X+2 2 X X+2 0 X 0 0 X+2 X+2 0 0
0 0 0 X 0 0 0 X X+2 X X X+2 0 X 2 0 X+2 X+2 X+2 2 X+2 2 2 X 0 X 0 2 2 X X+2 0 X X X+2 X+2 X+2 X X 2 0 X 0 X 0 0 X+2 0 X+2 2 2 X 2 X 0
0 0 0 0 X 0 X X X 2 X X X 2 2 X+2 X+2 2 2 0 X+2 X+2 0 2 X+2 0 0 X+2 X X+2 0 X+2 0 X 2 X+2 0 X 2 X+2 X X+2 2 X+2 2 X X+2 2 X 2 X 0 X+2 0 0
0 0 0 0 0 X X 2 X+2 X+2 X X X+2 0 X 2 2 2 X+2 2 X+2 0 X+2 0 0 0 X X X 0 X 0 X 2 X X X 0 X 2 X+2 0 0 2 X+2 2 0 0 2 X+2 X+2 0 X X 0
0 0 0 0 0 0 2 2 2 2 2 2 2 0 2 0 0 0 2 0 2 0 0 2 2 2 2 0 0 2 0 2 2 0 0 0 0 0 2 2 0 0 2 2 2 0 0 2 0 0 0 2 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+50x^44+118x^45+188x^46+292x^47+362x^48+452x^49+634x^50+810x^51+1147x^52+1432x^53+1742x^54+1930x^55+1725x^56+1556x^57+1131x^58+812x^59+617x^60+418x^61+325x^62+208x^63+172x^64+104x^65+71x^66+42x^67+22x^68+16x^69+4x^70+2x^71+1x^86
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 16.2 seconds.