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 X X X X X X X X X X X X X 2 X X X 2X 1 1 1 1 X
0 2X+2 0 2X+2 0 2X+2 0 2X+2 0 2X+2 0 2X+2 0 2X+2 0 2X+2 2X 2 2X 2 2X 2 2X 2 2X 2 2X 2 2X 2 2X 2 2X+2 2X+2 2X+2 2 2X+2 2X+2 2X+2 2 0 0 0 2X 0 0 2X 2X 2X 2X 0 0 0 2X+2 2X+2
0 0 2X 0 0 0 2X 0 0 2X 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 0 0 0 0 0 0 0 0 2X 2X 2X 2X 0 0 2X 2X 0 2X 2X 2X 0 0 0 2X 0 0 0
0 0 0 2X 0 0 0 2X 2X 2X 2X 2X 2X 0 2X 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 0 2X 2X 0 2X 0 0 0 2X 2X 0 2X
0 0 0 0 2X 2X 2X 2X 2X 0 0 2X 0 2X 2X 0 0 0 2X 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 0 0 2X 2X 0 2X 2X 0 0 0 0 2X 2X 0 0 0 2X 2X 0 0
generates a code of length 55 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 52.
Homogenous weight enumerator: w(x)=1x^0+37x^52+32x^53+192x^54+32x^55+180x^56+4x^58+19x^60+10x^62+2x^64+2x^70+1x^72
The gray image is a code over GF(2) with n=440, k=9 and d=208.
This code was found by Heurico 1.16 in 0.125 seconds.